Information content of partially rank-ordered set samples

Hatefi, Armin; Jozani, Mohammad Jafari

doi:10.1007/s10182-016-0277-9

Cited by 5 publications

(6 citation statements)

References 26 publications

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“…Otherwise, we have subsetting error and this PROS sample is called imperfect. To model an imperfect PROS sampling design, following [1,15] and [16], let α be a double stochastic misplacement probability matrix,…”

Section: Pros Sampling Designmentioning

confidence: 99%

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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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Section: Pros Sampling Designmentioning

confidence: 99%

“…He also showed that PROS sampling has some advantages over RSS. [15] and [16] showed that the Fisher information of PROS samples is larger than the Fisher information of RSS samples of the same size. Since 2011, PROS sampling design has been the subject of many studies.…”

Section: Introductionmentioning

confidence: 96%

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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“…For more information, see Chen et al 9 and Hatefi and Jafari Jozani. 10 Table 8 summarizes the averages, SDs and the percent SD reductions ofp mp relative top srs under different ranking models. Table 9 provides similar results forp reg , the multi-concomitant RSS estimator which uses the logistic regression models for the ranking purpose.…”

Section: Breast Cancer Data Analysismentioning

confidence: 99%

An improved procedure for estimation of malignant breast cancer prevalence using partially rank ordered set samples with multiple concomitants

Hatefi

Jozani

2015

Stat Methods Med Res

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Rank-based sampling designs are widely used in situations where measuring the variable of interest is costly but a small number of sampling units (set) can be easily ranked prior to taking the final measurements on them and this can be done at little cost. When the variable of interest is binary, a common approach for ranking the sampling units is to estimate the probabilities of success through a logistic regression model. However, this requires training samples for model fitting. Also, in this approach once a sampling unit has been measured, the extra rank information obtained in the ranking process is not used further in the estimation process. To address these issues, in this paper, we propose to use the partially rank-ordered set sampling design with multiple concomitants. In this approach, instead of fitting a logistic regression model, a soft ranking technique is employed to obtain a vector of weights for each measured unit that represents the probability or the degree of belief associated with its rank among a small set of sampling units. We construct an estimator which combines the rank information and the observed partially rank-ordered set measurements themselves. The proposed methodology is applied to a breast cancer study to estimate the proportion of patients with malignant (cancerous) breast tumours in a given population. Through extensive numerical studies, the performance of the estimator is evaluated under various concomitants with different ranking potentials (i.e. good, intermediate and bad) and tie structures among the ranks. We show that the precision of the partially rank-ordered set estimator is better than its counterparts under simple random sampling and ranked set sampling designs and, hence, the sample size required to achieve a desired precision is reduced.

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“…Nazari et al [9] have estimated the distribution function using PROS samples. Hatefi et al [10] have studied the information and uncertainty structures of PROS data.…”

Section: Introductionmentioning

confidence: 99%

Improved Kaplan-Meier Estimator in Survival Analysis Based on Partially Rank-Ordered Set Samples

Nematolahi

Nazari

Shayan

et al. 2020

Computational and Mathematical Methods in Medicine

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This study presents a novel methodology to investigate the nonparametric estimation of a survival probability under random censoring time using the ranked observations from a Partially Rank-Ordered Set (PROS) sampling design and employs it in a hematological disorder study. The PROS sampling design has numerous applications in medicine, social sciences and ecology where the exact measurement of the sampling units is costly; however, sampling units can be ordered by using judgment ranking or available concomitant information. The general estimation methods are not directly applicable to the case where samples are from rank-based sampling designs, because the sampling units do not meet the identically distributed assumption. We derive asymptotic distribution of a Kaplan-Meier (KM) estimator under PROS sampling design. Finally, we compare the performance of the suggested estimators via several simulation studies and apply the proposed methods to a real data set. The results show that the proposed estimator under rank-based sampling designs outperforms its counterpart in a simple random sample (SRS).

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Information content of partially rank-ordered set samples

Cited by 5 publications

References 26 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

An improved procedure for estimation of malignant breast cancer prevalence using partially rank ordered set samples with multiple concomitants

Improved Kaplan-Meier Estimator in Survival Analysis Based on Partially Rank-Ordered Set Samples

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