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Computational Statistics (09434062) 40(5)pp. 2729-2748
It is a common challenge in medical field to obtain the prevalence of a specific disease within a given population. To tackle this problem, researchers usually draw a random sample from the target population to obtain an accurate estimate of the proportion of diseased people. However, some limitations may occur in practice due to constraints, such as complexity or cost. In these situations, some alternative sampling techniques are needed to achieve precision with smaller sample sizes. One such approach is Neoteric Ranked Set Sampling (NRSS), which is a variation of Ranked Set Sampling (RSS) design. NRSS scheme involves selecting sample units using a rank-based method that incorporates auxiliary information to obtain a more informative sample. In this article, we focus on the problem of estimating the population proportion using NRSS. We develop an estimator for the population proportion using the NRSS design and establish some of its properties. We employ Monte Carlo simulations to compare the proposed estimator with competitors in Simple Random Sampling (SRS) and RSS designs. Our results demonstrate that statistical inference based on the introduced estimator can be significantly more efficient than its competitors in RSS and SRS designs. Finally, to demonstrate the effectiveness of the proposed procedure in estimating breast cancer prevalence within the target population, we apply it to analyze Wisconsin Breast Cancer data. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
This research investigates the construction of regression models for scenarios in which the response variable is inflated at specific points. To address this, we propose a comprehensive family of inflated distributions, which encompasses virtually all standard inflated distributions as special cases. The proposed family of distributions is applicable when the variable of interest is discrete, continuous, or a combination of both. We discuss parameter estimation, develop a regression model using the introduced family of distributions, and formulate an expectation-maximization (EM) algorithm to determine the maximum likelihood estimators of the proposed regression model. Additionally, we develop a general likelihood ratio test for the regression parameters. Finally, in two simulation scenarios and two real data sets, (obtained from the US National Center for Health Statistics (NCHS) and the residents of Olmsted County aged 50 or older), we analyse the performance of the proposed model. © 2025 Informa UK Limited, trading as Taylor & Francis Group.
Biometrical Journal (03233847) 67(2)
The mean residual life (MRL) function plays an important role in the summary and analysis of survival data. The main advantage of this function is that it summarizes the information in units of time instead of a probability scale, which requires careful interpretation. Ranked set sampling (RSS) is a sampling technique designed for situations, where obtaining precise measurements of sample units is expensive or difficult, but ranking them without referring to their accurate values is cost-effective or easy. However, the practical application of RSS is hindered because each sample unit is required to assign a unique rank. To alleviate this difficulty, Frey developed a novel variation of RSS, called RSS-t, that records and utilizes the tie structure in the ranking process. In this paper, we propose several different nonparametric estimators for the MRL function based on RSS-t. Then, we compare the proposed estimators with their counterparts in simple random sampling (SRS) and RSS, where tie information is not utilized. We also implemented our proposed estimators on a real data set related to patient waiting times for liver transplantation, to show their applicability and efficiency in practice. Our results show that using ties information leads to an improved statistical inference for the MRL function, and therefore a smaller sample size is needed to reach a predetermined precision. © 2025 Wiley-VCH GmbH.
Journal of Statistical Planning and Inference (03783758) 235
This paper focuses on drawing statistical inference based on a novel variant of maxima or minima nomination sampling (NS) designs. These sampling designs are useful for obtaining more representative sample units from the tails of the population distribution using the available auxiliary ranking information. However, one common difficulty in performing NS in practice is that the researcher cannot obtain a nominated sample unless he/she uniquely determines the sample unit with the highest or the lowest rank in each set. To overcome this problem, a variant of NS, which is called partial nomination sampling, is proposed, in which the researcher is allowed to declare that two or more units are tied in the ranks whenever he/she cannot find the sample unit with the highest or the lowest rank. Based on this sampling design, two asymptotically unbiased estimators are developed for the cumulative distribution function, which is obtained using maximum likelihood and moment-based approaches, and their asymptotic normalities are proved. Several numerical studies have shown that the proposed estimators have higher relative efficiencies than their counterparts in simple random sampling in analyzing either the upper or the lower tail of the parent distribution. The procedures that we developed are then implemented on a real dataset from the Third National Health and Nutrition Examination Survey (NHANES III) to estimate the prevalence of osteoporosis among adult women aged 50 and over. It is shown that in certain circumstances, the techniques that we have developed require only one-third of the sample size needed in SRS to achieve the desired precision. This results in a considerable reduction in time and cost compared to the standard SRS method. © 2024 Elsevier B.V.
Journal of Computational and Applied Mathematics (03770427) 458
In this work, we discuss a general class of estimators for the cumulative distribution function (CDF) based on judgment post stratification (JPS) sampling scheme, which includes both empirical and kernel distribution functions. Specifically, we obtain the expectation of the estimators in this class and show that they are asymptotically more efficient than their competitors in simple random sampling (SRS), as long as the rankings are better than random guessing. We find a mild condition that is necessary and sufficient for them to be asymptotically unbiased. We also prove that given the same condition, the estimators in this class are strongly uniformly consistent estimators of the true CDF, and converge in distribution to a normal distribution when the sample size approaches infinity. We then focus on the kernel distribution function (KDF) in the JPS design and obtain the optimal bandwidth. We next carry out a comprehensive Monte Carlo simulation to compare the performance of the KDF in the JPS design for different choices of sample size, set size, ranking quality, parent distribution, kernel function, as well as both perfect and imperfect rankings set-ups, with its counterpart in the SRS design. We find that the JPS estimator dramatically improves the efficiency of the KDF compared to its SRS competitor across a wide range of the settings. Finally, we apply the described procedure to a real dataset from a medical context to show its usefulness and applicability in practice. © 2024 Elsevier B.V.
Environmental and Ecological Statistics (13528505) 31(4)pp. 1039-1062
The volume under the receiver operating characteristic (ROC) surface (VUS) is a natural generalization of a classical tool, the area under the ROC curve from a disease with two statuses (e.g., healthy and diseased) to a disease with a three-class status (e.g., healthy, intermediate, and diseased) for evaluating the effectiveness of a continuous biomarker in discriminating the disease status. In this work, we discuss the problem of estimating VUS using ranked set sampling (RSS), a cost-efficient alternative to simple random sampling (SRS), which is applicable in situations in which the actual quantification of the biomarker is hard, time-consuming, costly or tedious but a small number of sample units can still be ordered without referring to their precise values. We develop several nonparametric estimators when SRS or RSS design is applied to each of the healthy, intermediate and diseased subpopulations. We study the properties of the proposed estimators, including unbiasedness, variance expression, asymptotic normality, and efficiency. Specifically, we show that the introduced estimators are at least as efficient as their SRS counterparts and often far more efficient under a large class of imperfect ranking models. Lastly, to demonstrate the applicability and efficiency of the introduced procedures in an environmental context, we apply them to a real environmental dataset, utilizing three of its five classes. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
International Journal of Biostatistics (15574679) 20(2)pp. 571-583
The mean residual lifetime (MRL) of a unit in a population at a given time t, is the average remaining lifetime among those population units still alive at the time t. In some applications, it is reasonable to assume that MRL function is a decreasing function over time. Thus, one natural way to improve the estimation of MRL function is to use this assumption in estimation process. In this paper, we develop an MRL estimator in ranked set sampling (RSS) which, enjoys the monotonicity property. We prove that it is a strongly uniformly consistent estimator of true MRL function. We also show that the asymptotic distribution of the introduced estimator is the same as the empirical one, and therefore the novel estimator is obtained "free of charge", at least in an asymptotic sense. We then compare the proposed estimator with its competitors in RSS and simple random sampling (SRS) using Monte Carlo simulation. Our simulation results confirm the superiority of the proposed procedure for finite sample sizes. Finally, a real dataset from the Surveillance, Epidemiology and End Results (SEER) program of the US National Cancer Institute (NCI) is used to show that the introduced technique can provide more accurate estimates for the average remaining lifetime of patients with breast cancer. © 2024 Walter de Gruyter GmbH, Berlin/Boston.
Journal of Applied Statistics (02664763) 51(13)pp. 2512-2528
The mean residual lifetime (MRL) of a unit is its expected additional lifetime provided that it has survived until time t. The MRL estimation problem has been frequently addressed in the literature since it has wide applications in statistics, reliability and survival analysis. In this paper, we consider the problem of estimating the MRL in ranked set sampling when actual quantifications of a concomitant variable are available. To exploit the additional information of the concomitant variable, we introduce several MRL estimators based on some regression techniques. We then compare them with the standard MRL estimator in simple random sampling using Monte Carlo simulation and a real dataset from the Surveillance, Epidemiology, and End Results Program. Our results indicate the superiority of the procedures that we have developed when the quality of ranking is fairly good. © 2024 Informa UK Limited, trading as Taylor & Francis Group.
Computational Statistics (09434062) 39(5)pp. 2721-2742
The area under a receiver operating characteristic (ROC) curve is frequently used in medical studies to evaluate the effectiveness of a continuous diagnostic biomarker, with values closer to one indicating better classification. Unfortunately, the standard statistical procedures based on simple random sampling (SRS) and ranked set sampling (RSS) techniques tend to be less efficient when the values of the area under a ROC curve (AUC) get closer to one. Thus, developing some statistical procedures for efficiently estimating the AUC when it is close to one is very important. In this paper, some estimators are developed using nomination sampling to assess AUC. The proposed AUC estimators are compared with their counterparts in SRS and RSS using Monte Carlo simulation. The results show that some of the estimators developed in this study considerably improve the efficiency of the AUC estimation when it is close to one. This substantially reduces the cost and time for the sample size needed to obtain the desired precision. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023.
Statistical Papers (09325026) 64(1)pp. 161-177
The mean past lifetime (MPL) is an important tool in reliability and survival analysis for measuring the average time elapsed since the occurrence of an event, under the condition that the event has occurred before a specific time t> 0. This article develops a nonparametric estimator for MPL based on observations collected according to ranked set sampling (RSS) design. It is shown that the proposed estimator is a strongly uniform consistent estimator of MPL. It is also proved that the introduced estimator tends to a Gaussian process under some mild conditions. A Monte Carlo simulation study is employed to evaluate the performance of the proposed estimator with its competitor in simple random sampling (SRS). Our findings show the introduced estimator is more efficient than its counterpart estimator in SRS as long as the quality of ranking is better than random. Finally, an illustrative example is provided to describe the potential application of the developed estimator in assessing the average time between the infection and diagnosis in HIV patients. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Hacettepe Journal of Mathematics and Statistics (2651477X) 51(6)pp. 1768-1779
Multistage pair ranked set sampling (MSPRSS) is a rank-based design that improves statistical inference with respect to simple random sampling of the same size. It is applicable when exact measurement is difficult, but judgment raking of the potential sample units can be done fairly accurately and easily. The ranking is usually performed based on personal judgment or a concomitant variable, and need not be totally free of errors. This article deals with estimating the cumulative distribution function in MSPRSS. The proposed estimator is theoretically compared with its contenders in the literature. The findings are supported by numerical evidence from simulation, and real data in the context of body fat analysis. Finally, a cost analysis is performed to show the advantage of the estimator. © 2022, Hacettepe University. All rights reserved.
Springer Proceedings in Mathematics and Statistics (21941009) 380pp. 53-64
In this work, we describe some goodness of fit tests for Cauchy distribution using ranked set sampling (RSS) design. The powers of the developed tests in RSS are compared with their counterparts in simple random sampling (SRS) for both perfect and imperfect ranking cases. It is found that the test based on Kullback–Leibler distance is much more powerful than its competitors in most of the cases considered. It also controls type I error well in the case of imperfect ranking. © 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
Statistical Papers (09325026) 63(6)pp. 1777-1799
Ranked set sampling (RSS) utilizes auxiliary information on the variable of interest so as to assist the experimenter in acquiring an informative sample from the population. The resulting sample has a stratified structure, and often improves statistical inference with respect to the simple random sample of comparable size. In RSS literature, there are some goodness-of-fit tests based on the empirical estimators of the in-stratum cumulative distribution functions (CDFs). Motivated by the fact that the in-stratum CDFs in RSS can be expressed as functions of the population CDF, some new tests are developed and their asymptotic properties are explored. An extensive simulation study is performed to evaluate properties of different testing procedures when the parent distribution is normal. It turns out that the proposed tests can be considerably more powerful than their contenders in many situations. An application in the context of fishery is also provided. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Statistical Methods in Medical Research (09622802) 31(8)pp. 1500-1514
In medical research, the receiver operating characteristic curve is widely used to evaluate accuracy of a continuous biomarker. The area under this curve is known as an index for overall performance of the biomarker. This article develops three new estimators of the area under the receiver operating characteristic curve in ranked set sampling. The first estimator is obtained under normality assumption. The two other estimators are constructed by applying a Box–Cox transformation on data, and then using either a parametric estimator or a kernel-density-based estimator. A simulation study is carried out to compare the proposed estimators with those available in the literature. It emerges that the new estimators offer some advantages in specific situations. Application of the methods is demonstrated using real data in the context of medicine. © The Author(s) 2022.
Communications in Statistics: Simulation and Computation (03610918) 51(5)pp. 2747-2768
This article studies interval estimation of the population mean in ranked set sampling. Eight types of confidence intervals are considered which are based on asymptotic theory, resampling methods, or a combination of them. A comprehensive simulation study is conducted to investigate performance of these intervals, and to deal with some limitations of a relevant work in the literature. Lastly, a data example is presented to illustrate the procedures. © 2020 Taylor & Francis Group, LLC.
Soft Computing (14327643) 26(7)pp. 3161-3170
It is highly important for governments and health organizations to monitor the prevalence of breast cancer as a leading source of cancer-related death among women. However, the accurate diagnosis of this disease is expensive, especially in developing countries. This article concerns a cost-efficient method for estimating prevalence of breast cancer, when diagnosis is based on a comprehensive biopsy procedure. Multistage ranked set sampling (MSRSS) is utilized to develop a proportion estimator. This design employs imprecise rankings based on some visually assessed cytological covariates, so as to provide the experimenter with a more informative sample. Theoretical properties of the proposed estimator are explored. Evidence from numerical studies is reported. The developed procedure can be substantially more efficient than its competitor in simple random sampling (SRS). In some situations, the proportion estimation in MSRSS needs around 76% fewer observations than that in SRS, given a precision level. Thus, using MSRSS may lead to a considerable reduction in cost with respect to SRS. In many medical studies, e.g., diagnosing breast cancer based on a full biopsy procedure, exact quantification is difficult (costly and/or time-consuming), but the potential sample units can be ranked fairly accurately without actual measurements. In this setup, multistage ranked set sampling is an appropriate design for developing cost-efficient statistical methods. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Statistical Papers (09325026) 62(5)pp. 2453-2471
It has been shown in the literature that judgment post stratification (JPS) sampling design often leads to more efficient statistical inference than what is possible to obtain in simple random sampling (SRS) design of comparable size. Since the JPS is a cost-efficient sampling design, a large enough sample size may not be available to use normal theory of the estimators. In this paper, we describe two bootstrap methods for JPS sampling scheme, one of which has been already used in the literature without studying its consistency and the other is new. We also show that both bootstrap approaches are consistent. We then investigate the use of the bootstrap methods for constructing confidence intervals for the population mean and compare them with the confidence interval of the population mean obtained via normal approximation (NA) method using Monte Carlo simulation. It is found that for the asymmetric distributions, one of the bootstrap methods we describe in the paper often leads to a closer coverage probability (CP) to the nominal level than NA method. Finally, a real dataset is analysed for illustration. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
Brazilian Journal of Probability and Statistics (01030752) 35(2)pp. 375-391
This work deals with problem of estimating the odds using judgment post stratification (JPS) sampling design. Several estimators of the odds are described and the asymptotic normality of each of them is established. Monte Carlo simulation study is then used to compare different estimators of the odds in the JPS with the standard estimator in simple random sampling (SRS) with replacement for both perfect/imperfect ranking and for both JPS data with/without empty strata. The comparison results indicate that the estimators developed here can be highly more efficient than their SRS counterpart in some certain circumstances. Finally, a real dataset from the third National Health and Nutrition Examination Survey (NHANES III) is employed for illustration purposes. © Brazilian Statistical Association, 2021.
International Journal of Biostatistics (15574679) 17(1)pp. 139-152
Ranked set sampling (RSS), known as a cost-effective sampling technique, requires that the ranker gives a complete ranking of the units in each set. Frey (2012) proposed a modification of RSS based on partially ordered sets, referred to as RSS-t in this paper, to allow the ranker to declare ties as much as he/she wishes. We consider the problem of estimating the area under a receiver operating characteristics (ROC) curve using RSS-t samples. The area under the ROC curve (AUC) is commonly used as a measure for the effectiveness of diagnostic markers. We develop six nonparametric estimators of the AUC with/without utilizing tie information based on different approaches. We then compare the estimators using a Monte Carlo simulation and an empirical study with real data from the National Health and Nutrition Examination Survey. The results show that utilizing tie information increases the efficiency of estimating the AUC. Suggestions about when to choose which estimator are also made available to practitioners. © 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.
Soft Computing (14327643) 25(13)pp. 8007-8013
Ranked set sampling (RSS) utilizes imprecise rankings on the variable of interest in order to draw an informative sample from the target population. The resulting sample, consisting of independent judgment order statistics, resembles a stratified random sample. Estimating the variances of strata is an important problem in RSS. The standard method is based on the sample variance of units in each stratum. A plug-in estimator is also available in the literature that remedies some shortcomings of the standard estimator. We adjust the latter estimator using kernel estimator of the distribution function. The developed estimator is shown to be consistent, and its performance is investigated by means of simulation. It turns out that our proposal can be considerably more efficient than the existing estimators when perfect or nearly perfect ranking holds. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Statistical Papers (09325026) 62(4)pp. 1753-1776
The receiver operating characteristic (ROC) curve is an important tool for assessing the discrimination power of a continuous biomarker. The area under the ROC curve is a well-known index for effectiveness of the biomarker. This article deals with estimating the aforesaid measure under a rank-based sampling design called multistage ranked set sampling. A nonparametric estimator using kernel density estimation is developed, and some theoretical results about it are established. Simulation studies show that the proposed estimator can be substantially more efficient than its alternative in simple random sampling. The methodology is illustrated with data from the National Health and Nutrition Examination Survey. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
AStA Advances in Statistical Analysis (18638171) 104(3)pp. 485-502
In this article, we consider the problem of estimating cumulative distribution function (CDF) and a reliability parameter using moving extreme ranked set sampling (MERSS). Two different CDF estimators are described and compared with their competitors in simple random sampling (SRS) and ranked set sampling (RSS). It turns out the CDF estimators in MERSS can be more efficient than their competitors in SRS and RSS at a point in a particular tail of the distribution when the quality of rankings is sufficiently good. Motivated by this efficiency gain, we develop some estimators for the stress-strength probability using MERSS. The suggested estimators are then compared with their counterparts in the literature via Monte Carlo simulation. Finally, a real dataset is used to show the applicability of the developed procedures. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
Computational Statistics (09434062) 35(4)pp. 1785-1803
M-estimator for symmetric location families in ranked set sampling has been studied in the literature. Estimating asymptotic variance of this estimator has not been addressed yet. To fill this gap, we develop two consistent estimators in this article. The proposed estimators are then utilized to construct confidence intervals for the location parameter. Monte Carlo simulations are employed to assess performance of the intervals. Finally, an empirical study is presented for illustration. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
Statistical Papers (09325026) 61(2)pp. 851-867
This article concerns estimation of a symmetric distribution function under multistage ranked set sampling. A nonparametric estimator is developed and its theoretical properties are explored. Performance of the suggested estimator is further evaluated using numerical studies. © 2017, Springer-Verlag GmbH Germany, part of Springer Nature.
Annals of the Institute of Statistical Mathematics (00203157) 72(1)pp. 157-185
Consider independent observations (Xi, Ri) with random or fixed ranks Ri, while conditional on Ri, the random variable Xi has the same distribution as the Ri-th order statistic within a random sample of size k from an unknown distribution function F. Such observation schemes are well known from ranked set sampling and judgment post-stratification. Within a general, not necessarily balanced setting we derive and compare the asymptotic distributions of three different estimators of the distribution function F: a stratified estimator, a nonparametric maximum-likelihood estimator and a moment-based estimator. Our functional central limit theorems generalize and refine previous asymptotic analyses. In addition, we discuss briefly pointwise and simultaneous confidence intervals for the distribution function with guaranteed coverage probability for finite sample sizes. The methods are illustrated with a real data example, and the potential impact of imperfect rankings is investigated in a small simulation experiment. © 2018, The Institute of Statistical Mathematics, Tokyo.
Statistical Papers (09325026) 61(2)pp. 767-785
We propose an unbiased estimator for P(X> Y) and obtain an exact expression for its variance, based on judgement post stratification (JPS) sampling scheme. We then prove that the introduced estimator is consistent and establish its asymptotic normality. We show that the proposed estimator is at least as efficient asymptotically as its counterpart in simple random sampling (SRS), regardless of the quality of the rankings. For finite sample sizes, a Monte Carlo simulation study and a real data set are employed to show the preference of the JPS estimator to its SRS competitor in a wide range of settings. © 2017, Springer-Verlag GmbH Germany.
Statistical Methods in Medical Research (09622802) 29(1)pp. 165-177
This article studies the properties of the maximum likelihood estimator of the population proportion in ranked set sampling with extreme ranks. The maximum likelihood estimator is described and its asymptotic distribution is derived. Finite sample size properties of the estimator are investigated using simulation studies. It turns out that the proposed estimator is substantially more efficient than its simple random sampling and ranked set sampling analogs, as the true population proportion tends to zero/unity. The method is illustrated using data from the National Health and Nutrition Examination Survey. © The Author(s) 2019.
Iranian Journal of Science and Technology, Transaction A: Science (10286276) 43(6)pp. 3017-3028
This article concerns the problem of interval estimation for the population quantiles in ranked set sampling. Some intervals are developed using asymptotic normality of nonparametric quantile estimator and/or resampling methods. The proposed procedures are evaluated in terms of coverage rate and average length. Some comparisons with analogous intervals in simple random sampling are also made. Finally, a medical data set is used to illustrate application of the intervals. © 2019, Shiraz University.
Probability and Mathematical Statistics (02084147) 39(1)pp. 1-18
Ranked set sampling (RSS) is a data collection method that allows us to direct attention toward measurements of more representative sample units. This article deals with estimating a time-dependent reliability measure under a generalization of the RSS. Some results concerning optimal properties of the proposed estimator are presented. Monte Carlo simulation is employed to assess performance of the estimator. A sport data set is finally analyzed. © 2019, Wydawnictwo Uniwersytetu Wroclawskiego Sp. z o.o.. All rights reserved.
Statistical Papers (09325026) 60(6)pp. 2141-2159
In this paper, we develop a nonparameteric cumulative distribution function (CDF) estimator for pair ranked set sampling (PRSS) design. We show that the proposed estimator is consistent and establish its asymptotic normality. We then use the proposed estimator for developing some goodness of fit tests for testing exponentiality. We show that the proposed tests are more powerful than their counterparts in simple random sampling (SRS) and ranked set sampling (RSS) schemes. © 2017, Springer-Verlag Berlin Heidelberg.
Statistical Methods in Medical Research (09622802) 28(1)pp. 223-234
Rank-based sampling methods are applicable in settings where precise measurements are expensive, but small sets of units can be accurately ranked at negligible cost. This article introduces one such a design, called multistage pair ranked set sampling. It mitigates ranking burden associated with a competitor scheme, namely multistage ranked set sampling. The mean estimator in multistage pair ranked set sampling is unbiased, and under perfect rankings has variance no larger than its simple random sampling counterpart. Although the suggested mean estimator is outperformed by its multistage ranked set sampling analog in terms of precision under perfect rankings, the situation may be reversed if cost considerations are taken into account. The methodology is illustrated using a medical dataset. © The Author(s) 2017.
Computational Statistics and Data Analysis (01679473) 135pp. 35-55
The mean residual life (MRL) of a nonnegative random variable X plays an important role in various disciplines such as reliability, survival analysis, and extreme value theory. This paper deals with the problem of estimating the MRL in ranked set sampling (RSS) design. An RSS-based estimator for MRL is proposed and its properties are investigated. For finite sample sizes, a Monte Carlo simulation study is carried out to show that the resulting estimator is more efficient than its counterpart in simple random sampling (SRS) design. It is proved that the proposed estimator asymptotically follows a Gaussian process and its asymptotic variance is no larger than its counterpart in the SRS design, regardless of the quality of ranking. Different methods of constructing a confidence interval for MRL in the RSS and SRS designs are then discussed. It is observed that while both the RSS and SRS-based confidence intervals do not control the nominal confidence level equally well, the RSS-based confidence intervals have generally shorter lengths than those in the SRS scheme. Finally, a potential application in the context of medical studies is presented for illustration purpose. © 2019 Elsevier B.V.
Journal Of King Saud University - Science (10183647) 31(4)pp. 1167-1174
This article deals with goodness-of-fit test for the Cauchy distribution. Six new tests based on Kullback-Leibler information are proposed, and shown to be consistent. Monte Carlo evidence indicates that the tests have satisfactory performances against symmetric alternatives. An empirical application to quantitative finance is provided. © 2019 The Authors
Statistical Papers (09325026) 59(3)pp. 861-891
In this article, a dynamic reliability measure based on ranked set sampling is introduced, and its properties are investigated in theory and simulation. The results support the preference of the suggested index over the analogous one in simple random sampling. A data set from an agricultural experiment is analyzed for illustration. © 2016, Springer-Verlag Berlin Heidelberg.
Hacettepe Journal of Mathematics and Statistics (2651477X) 47(3)pp. 755-761
Ranked set sampling (RSS) is a data collection method designed to exploit auxiliary ranking information. In this paper, a new estimator of distribution function is proposed when RSS is done by using a con-comitant variable. It is shown by simulation study that the alternative estimator can be considerably more efficient than the standard one, especially when the rankings are perfect. © 2018, Hacettepe University. All rights reserved.
Filomat (03545180) 32(4)pp. 1455-1463
This article concerns reliability estimation in two-parameter exponential distributions setup with known scale parameters, and unknown location parameters. Based on the uniformly minimum variance unbiased estimator, we propose a new estimator and study its theoretical properties. Simulation results reveal that the suggested estimator could be highly efficient. © 2018, University of Nis. All rights reserved.
Journal of Applied Statistics (02664763) 45(3)pp. 426-437
In this paper, we consider the problem of estimating the population proportion in pair ranked set sampling design. An unbiased estimator for the population proportion is proposed, and its theoretical properties are studied. It is shown that the estimator is more (less) efficient than its counterpart in simple random sampling (ranked set sampling). Asymptotic normality of the estimator is also established. Application of the suggested procedure is illustrated using a data set from an environmental study. © 2017 Informa UK Limited, trading as Taylor & Francis Group.
Electronic Journal of Applied Statistical Analysis (20705948) 11(1)pp. 185-195
Some goodness of fit tests for logistic distribution based on Phi-divergence are developed. The powers of the introduced tests are compared with some traditional goodness of fit tests including Kolmogorov-Smirnov, Anderson- Darling and Cramer-von Mises tests for logistic distribution using Monte Carlo simulation. It is shown the proposed tests have good performance as compared with their competitors in the literature. A real data set is used for illustration. © 2018. University of Salento.
Computational Statistics (09434062) 33(3)pp. 1325-1348
This article deals with constructing a confidence interval for the reliability parameter using ranked set sampling. Some asymptotic and resampling-based intervals are suggested, and compared with their simple random sampling counterparts using Monte Carlo simulations. Finally, the methods are applied on a real data set in the context of agriculture. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
REVSTAT-Statistical Journal (16456726) 16(4)pp. 463-474
We develop parametric and location-scale free tests of perfect judgment ranking based on ordered ranked set samples. The tests are based on the differences between the elements of the ordered ranked set samples and those of the original ranked set samples. We compare our proposed tests with the best existing tests of perfect judgment ranking in the literature by using Monte Carlo simulation. Our simulation results show that the proposed tests behave favorably in comparison with their leading competitors, especially under the fraction of neighbor rankings model. In comparison to the nonparametric competitors, the proposed tests have the advantage of not needing randomization to attain a specific size. © 2018, National Statistical Institute. All rights reserved.
Computational Statistics (09434062) 33(3)pp. 1349-1366
Ranked set sampling (RSS) is a statistical technique that uses auxiliary ranking information of unmeasured sample units in an attempt to select a more representative sample that provides better estimation of population parameters than simple random sampling. However, the use of RSS can be hampered by the fact that a complete ranking of units in each set must be specified when implementing RSS. Recently, to allow ties declared as needed, Frey (Environ Ecol Stat 19(3):309–326, 2012) proposed a modification of RSS, which is to simply break ties at random so that a standard ranked set sample is obtained, and meanwhile record the tie structure for use in estimation. Under this RSS variation, several mean estimators were developed and their performance was compared via simulation, with focus on continuous outcome variables. We extend the work of Frey (2012) to binary outcomes and investigate three nonparametric and three likelihood-based proportion estimators (with/without utilizing tie information), among which four are directly extended from existing estimators and the other two are novel. Under different tie-generating mechanisms, we compare the performance of these estimators and draw conclusions based on both simulation and a data example about breast cancer prevalence. Suggestions are made about the choice of the proportion estimator in general. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
Statistics (02331888) 52(4)pp. 750-768
The authors develop a kernel-based estimator of a dynamic reliability measure for use with independent ranked set samples. The estimator is in the form of a ratio, whose numerator and denominator are shown to outperform their rivals based on simple random samples. Some asymptotic properties about the proposed estimator are also established. Simulation studies reveal finite-sample properties of the estimator. The technique is finally applied on an agricultural data set. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
Statistical Papers (09325026) 59(3)pp. 1085-1100
We develop some nonparametric tests of perfect judgment ranking for judgment post stratification sampling scheme. We show that the best proposed test beats the best existing nonparametric test of perfect judgment ranking in ranked set sampling applied to the judgment post stratification case by conditioning on the observed stratum sizes. © 2016, Springer-Verlag Berlin Heidelberg.
Communications in Statistics - Theory and Methods (03610926) 47(24)pp. 5904-5915
Stratified pair ranked set sampling is introduced and applied in estimating the population mean. Mathematical properties of the suggested estimator are treated. The estimator and its competitors are also compared through some numerical studies. Usefulness of the proposed design is illustrated using a cost analysis. © 2018, © 2018 Taylor & Francis Group, LLC.
Electronic Journal of Applied Statistical Analysis (20705948) 10(2)pp. 349-373
There is abundant and increasing evidence that the lognormal distribution can account for random variation present in the data from many scientific fields. In the light of this exibility for modeling, this article deals with goodness-of-fit tests for the lognormal distribution. Several testing procedures are compared by means of extensive simulation. Lastly, an actuarial data set is analyzed for illustration. © Universitá del Salento.
Statistics and Probability Letters (01677152) 129pp. 28-33
We propose a new estimator for the population proportion using a concomitant-based ranked set sampling (RSS) scheme. Simulation results show that the new estimator beats the standard estimator in the RSS as long as the ranking quality is fairly good. © 2017 Elsevier B.V.
Revista Colombiana de Estadistica (01201751) 40(2)pp. 223-241
This article deals with entropy estimation using ranked set sampling (RSS). Some estimators are developed based on the empirical distribution function and its nonparametric maximum likelihood competitor. The suggested entropy estimators have smaller root mean squared errors than the other entropy estimators in the literature. The proposed estimators are then used to construct goodness of fit tests for inverse Gaussian distribution. © 2017, Universidad Nacional de Colombia. All rights reserved.
Computational Statistics and Data Analysis (01679473) 112pp. 257-269
This paper is concerned with the problem of estimating a population proportion p in a judgment post-stratification (JPS) sampling scheme. Different proportion estimators are considered, among which some are specifically designed to deal with JPS samples with empty strata; and asymptotic normality is established for each. A Monte Carlo simulation study and two examples using data from medical studies are employed to examine the performance of these proportion estimators under both perfect and imperfect ranking and for JPS data both with and without empty strata. It is shown that the JPS scheme improves estimation of the population proportion in a very wide range of settings as compared to simple random sampling (SRS). Also, findings about the relative performance of the different estimators are provided to help practitioners determine which estimator should be used under certain situations. © 2017 Elsevier B.V.
Revista Colombiana de Estadistica (01201751) 40(2)pp. 279-290
In this paper, we develop some goodness of fit tests for Rayleigh distribution based on Phi-divergence. Using Monte Carlo simulation, we compare the power of the proposed tests with some traditional goodness of fit tests including Kolmogorov-Smirnov, Anderson-Darling and Cramer von-Mises tests. The results indicate that the proposed tests perform well as compared with their competing tests in the literature. Finally, the new procedures are illustrated via two real data sets. © 2017, Universidad Nacional de Colombia. All rights reserved.
Investigacion Operacional (02574306) 38(4)pp. 366-376
The ranked set sampling (RSS) method is more efficient than the commonly used simple random sampling (SRS) method. In this paper, some new goodness-of-fit tests based on the sample entropy and empirical distribution function for the Laplace distribution using ranked set sampling (RSS) are suggested. The newly suggested tests based on RSS are compared with their simple random sampling (SRS) competitors. The critical values of the corresponding test statistic are computed for each method and the powers of the tests are obtained based on different alternatives. Simulation results indicate that RSS tests are more powerful than their SRS counterparts.
Journal of Applied Statistics (02664763) 44(6)pp. 1106-1121
Some goodness-of-fit procedures for the Cauchy distribution are presented. The power comparisons indicate that the new tests possess good performances among the competitors, especially against symmetric alternatives. A financial data set is analyzed for illustration. © 2016 Informa UK Limited, trading as Taylor & Francis Group.
REVSTAT-Statistical Journal (16456726) 15(4)pp. 565-581
A nonparametric reliability estimator based on multistage ranked set sampling is developed. It is shown that the estimator is unbiased and its efficiency relative to the simple random sampling rival is increasing in the number of stages. Numerical experiments are used to illustrate the theoretical findings. The suggested procedure is applied on a sport data set. © 2017, National Statistical Institute. All rights reserved.
Journal of the Korean Statistical Society (12263192) 45(1)pp. 25-32
In this paper, we develop a nonparametric variance estimator for judgment post stratification sampling scheme. The estimator is obtained by using the fact that the distributions of post strata are often stochastically ordered. We prove that our estimator is consistent. Our simulation results indicate that the proposed estimator has good performance in comparison with its leading competitors in the literature. © 2015 The Korean Statistical Society.
Pakistan Journal Of Statistics And Operation Research (18162711) 12(1)pp. 25-39
In this paper, different goodness of fit tests for the Rayleigh distribution are considered based on simple random sampling (SRS) and ranked set sampling (RSS) techniques. The performance of the suggested estimators is evaluated in terms of the power of the tests by using Monte Carlo simulation. It is found that the suggested RSS tests perform better than their counterparts in SRS.
Pakistan Journal Of Statistics And Operation Research (18162711) 12(4)pp. 625-637
This article concerns entropy estimation using judgment post stratification sampling scheme. Some nonparametric estimators are developed and shown to be consistent. Monte Carlo simulations are used to compare these estimators with their competitors in simple random sampling. The results indicate the preference of the new estimators. © 2016, Pak.j.stat.oper.res. All rights reserved.
SORT (16962281) 40(2)pp. 243-266
This article is directed at the problem of reliability estimation using ranked set sampling. A non-parametric estimator based on kernel density estimation is developed. The estimator is shown to be superior to its analog in simple random sampling. Monte Carlo simulations are employed to assess performance of the proposed estimator. Two real data sets are analysed for illustration. © 2016, Institut d'Estadistica de Catalunya. All rights reserved.
Hacettepe Journal of Mathematics and Statistics (2651477X) 45(6)pp. 1891-1905
The purpose of this study is to suggest a new modification of the usual ranked set sampling (RSS) method, namely; neoteric ranked set sampling (NRSS) for estimating the population mean and variance. The performances of the empirical mean and variance estimators based on NRSS are compared with their counterparts in ranked set sampling and simple random sampling (SRS) via Monte Carlo simulation. Simulation results indicate that the NRSS estimators perform much better than their counterparts using RSS and SRS designs when the ranking is perfect. When the ranking is imperfect, the NRSS estimators are still superior to their counterparts in ranked set sampling and simple random sampling methods. These findings show that the NRSS provides a uniform improvement over RSS without any additional costs. Finally, an illustrative example of a real data is provided to show the application of the new method in practice. © 2016, Hacettepe University. All rights reserved.
Journal of Statistical Computation and Simulation (00949655) 85(16)pp. 3191-3205
In this paper, we first introduce new entropy estimators for distributions with known and bounded supports. Our estimators are obtained by using constrained maximum likelihood estimation of cumulative distribution function for absolutely continuous distributions with known and bounded supports. We prove the consistency of our estimators. Then, we propose uniformity tests based on the proposed entropy estimators and compare their powers with the powers of other tests of uniformity. Our simulation results show that the proposed entropy estimators perform well in estimating entropy and testing uniformity. © 2014 Taylor & Francis.
Statistics and Probability Letters (01677152) 105pp. 1-5
We propose a nonparametric variance estimator when ranked set sampling (RSS) and judgment post stratification (JPS) are applied by measuring a concomitant variable. Our proposed estimator is obtained by conditioning on observed concomitant values and using nonparametric kernel regression. © 2015 Elsevier B.V.
Communications in Statistics - Theory and Methods (1532415X) 43(21)pp. 4589-4611
Many techniques based on data which are drawn by Ranked Set Sampling (RSS) scheme assume that the ranking of observations is perfect. Therefore it is essential to develop some methods for testing this assumption. In this article, we propose a parametric location-scale free test for assessing the assumption of perfect ranking. The results of a simulation study in two special cases of normal and exponential distributions indicate that the proposed test performs well in comparison with its leading competitors. Copyright © Taylor & Francis Group, LLC.
Statistics and Probability Letters (01677152) 82(12)pp. 2213-2220
We improve three tests of perfect ranking in ranked set sampling proposed by Li and Balakrishnan (2008) using a permutation approach. This simple way of extending all three concepts to comparisons across different cycles increases the power. Two of the proposed tests are equivalent to tests from the literature, which were derived differently and are therefore generalized by the permutation-based tests. © 2012 Elsevier B.V.
Journal of Statistical Computation and Simulation (15635163) 82(11)pp. 1701-1713
In this paper, we first introduce two new estimators for estimating the entropy of absolutely continuous random variables. We then compare the introduced estimators with the existing entropy estimators, including the first of such estimators proposed by Dimitriev and Tarasenko [On the estimation functions of the probability density and its derivatives, Theory Probab. Appl. 18 (1973), pp. 628-633]. We next propose goodness-of-fit tests for normality based on the introduced entropy estimators and compare their powers with the powers of other entropy-based tests for normality. Our simulation results show that the introduced estimators perform well in estimating entropy and testing normality. © 2012 Copyright Taylor and Francis Group, LLC.
Journal of Statistical Computation and Simulation (15635163) 81(12)pp. 2077-2093
In this paper, we first propose a new estimator of entropy for continuous random variables. Our estimator is obtained by correcting the coefficients of Vasicek's [A test for normality based on sample entropy, J. R. Statist. Soc. Ser. B 38 (1976), pp. 54-59] entropy estimator. We prove the consistency of our estimator. Monte Carlo studies show that our estimator is better than the entropy estimators proposed by Vasicek, Ebrahimi et al. [Two measures of sample entropy, Stat. Probab. Lett. 20 (1994), pp. 225-234] and Correa [A new estimator of entropy, Commun. Stat. Theory Methods 24 (1995), pp. 2439-2449] in terms of root mean square error. We then derive the non-parametric distribution function corresponding to our proposed entropy estimator as a piece-wise uniform distribution. We also introduce goodness-of-fit tests for testing exponentiality and normality based on the said distribution and compare its performance with their leading competitors. © 2011 Copyright Taylor and Francis Group, LLC.
Forum for Interdisciplinary Mathematics (23646748) pp. 57-77
Ranked set sampling (RSS) is a cost efficient design that has been widely used in agriculture, forestry, ecological and environmental sciences. Frey (Environmental and Ecological Statistics 19(3):309–326, 2012) proposed a sampling scheme based on to allow for partially ordered sets. This scheme permits a ranker to declare ties and then record the tie structure for potential use in statistical analysis. We first introduce two nonparametric maximum likelihood estimators (MLEs) of the population cumulative distribution function (CDF) that incorporate the information for partially ordered sets. We compare the proposed MLEs with the standard nonparametric MLE of the CDF (without utilizing tie information) via Monte Carlo simulation. Motivated by good performance of the new CDF estimators, we further derive two mean estimators for partially ordered sets. Our numerical results from both simulation and real data show that the proposed estimators outperform their competitors provided that the quality of ranking is not low. © Springer Nature Singapore Pte Ltd 2020.
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