Sampling from partially rank-ordered sets

Öztürk, Ömer

doi:10.1007/s10651-010-0161-9

Cited by 43 publications

(18 citation statements)

References 15 publications

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“…The proof is essentially the same as the one given by [22] for h(x) = x which we present here for the sake of completeness. Part (i) is an immediate consequence of Lemma 1.…”

Section: Some Notations and Preliminary Resultsmentioning

confidence: 76%

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Nonparametric density estimation using partially rank-ordered set samples with application in estimating the distribution of wheat yield

Nazari¹,

Jozani²,

Kharrati-Kopaei³

2014

Electron. J. Statist.

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We study nonparametric estimation of an unknown density function f based on the ranked-based observations obtained from a partially rank-ordered set (PROS) sampling design. PROS sampling design has many applications in environmental, ecological and medical studies where the exact measurement of the variable of interest is costly but a small number of sampling units can be ordered with respect to the variable of interest by any means other than actual measurements and this can be done at low cost. PROS observations involve independent order statistics which are not identically distributed and most of the commonly used nonparametric techniques are not directly applicable to them. We first develop a kernel density estimator of f based on an imperfect PROS sampling procedure and study its theoretical properties. Then, we consider the problem when the underlying distribution is assumed to be symmetric and introduce some plug-in kernel density estimators of f . We use an EM type algorithm to estimate misplacement probabilities associated with an imperfect PROS design. Finally, we expand on various numerical illustrations of our results via several simulation studies and a case study to estimate the distribution of wheat yield using the total acreage of land which is planted in wheat as an easily obtained auxiliary information. Our results show that the PROS density estimate performs better than its SRS and RSS counterparts.

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“…The proof is essentially the same as the one given by [22] for h(x) = x which we present here for the sake of completeness. Part (i) is an immediate consequence of Lemma 1.…”

Section: Some Notations and Preliminary Resultsmentioning

confidence: 76%

“…[22] introduced PROS sampling procedure as a generalization of the ranked set sampling (RSS) design. To obtain a ranked set sample of size n one can proceed as follows.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric density estimation using partially rank-ordered set samples with application in estimating the distribution of wheat yield

Nazari¹,

Jozani²,

Kharrati-Kopaei³

2014

Electron. J. Statist.

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“…Forcing rankers to declare unique ranks can lead to inflated within-set judgment ranking error and consequently to invalid statistical inference. Partially rank-ordered set (PROS) sampling design is a generalization of ranked set sampling, due to Ozturk (2011), which is aimed at reducing the impact of ranking error and the burden on rankers by not requiring them to provide a full ranking of all the units in each set. Under PROS sampling technique, rankers have more flexibility by being able to divide the sampling units into subsets of pre-specified sizes.…”

Section: Introductionmentioning

confidence: 99%

Information content of partially rank-ordered set samples

Hatefi

Jozani

2016

AStA Adv Stat Anal

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Partially rank-ordered set (PROS) sampling is a generalization of ranked set sampling in which rankers are not required to fully rank the sampling units in each set, hence having more flexibility to perform the necessary judgemental ranking process.The PROS sampling has a wide range of applications in different fields ranging from environmental and ecological studies to medical research and it has been shown to be superior over ranked set sampling and simple random sampling for estimating the population mean. We study the Fisher information content and uncertainty structure of the PROS samples and compare them with those of simple random sample (SRS) and ranked set sample (RSS) counterparts of the same size from the underlying population. We study the uncertainty structure in terms of the Shannon entropy, Rényi entropy and Kullback-Leibler (KL) discrimination measures. Several examples including the FI of PROS samples from the location-scale family of distributions as well as a regression model are discussed.

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“…Thus, it is crucial to minimize the judgement ranking error as much as possible. In order to achieve this goal, Ozturk () introduced a new sampling design in which a ranker is allowed to declare ties among units in subsets of prespecified sizes. The tied units in these subsets are partially rank ordered so that any unit in the subset h has a smaller rank than any other unit in the subset h ′, h < h ′.…”

Section: Introductionmentioning

confidence: 99%

Mixture Model Analysis of Partially Rank‐Ordered Set Samples: Age Groups of Fish from Length‐Frequency Data

Hatefi

Jozani

Öztürk

2015

Scandinavian J Statistics

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We present a novel methodology for estimating the parameters of a finite mixture model (FMM) based on partially rank-ordered set (PROS) sampling and use it in a fishery application. A PROS sampling design first selects a simple random sample of fish and creates partially rank-ordered judgement subsets by dividing units into subsets of prespecified sizes. The final measurements are then obtained from these partially ordered judgement subsets. The traditional expectation-maximization algorithm is not directly applicable for these observations. We propose a suitable expectation-maximization algorithm to estimate the parameters of the FMMs based on PROS samples. We also study the problem of classification of the PROS sample into the components of the FMM. We show that the maximum likelihood estimators based on PROS samples perform substantially better than their simple random sample counterparts even with small samples. The results are used to classify a fish population using the length-frequency data.

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Sampling from partially rank-ordered sets

Cited by 43 publications

References 15 publications

Nonparametric density estimation using partially rank-ordered set samples with application in estimating the distribution of wheat yield

Nonparametric density estimation using partially rank-ordered set samples with application in estimating the distribution of wheat yield

Information content of partially rank-ordered set samples

Mixture Model Analysis of Partially Rank‐Ordered Set Samples: Age Groups of Fish from Length‐Frequency Data

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