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

Statistical process monitoring (SPM) and designing control charts include measuring quality characteristics by considering the time and cost constraints. Ranked set sampling (RSS) is a very efficient and an inexpensive approach in obtaining a more representative sample when the actual measurement of the sampling units is too expensive or destructive, where it is easier to rank the observations. Since 1997, when the first paper on designing control charts based on the RSS scheme was presented, a significant number of papers have been published in this area. This paper provides a literature review on using the RSS schemes in designing control charts. Relevant papers are classified and analyzed to identify the research gaps and provide recommendations and directions for future studies.

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“…This gives one cycle of the PROS sampling approach. The whole procedure can be repeated r times to get a PROS of size

rm

{X_{PROS}} = \{ {{X_{[ {{d_i}} ]j}};i = 1, \ldots ,m;j = 1, \ldots ,r} \}

76 …”

Section: Ranked Set Samplingmentioning

confidence: 99%

“…The whole procedure can be repeated 𝑟 times to get a PROS of size 𝑟𝑚, 𝑋 𝑃𝑅𝑂𝑆 = {𝑋 [𝑑 𝑖 ]𝑗 ; 𝑖 = 1, … , 𝑚; 𝑗 = 1, … , 𝑟}. 76 2.1.6 Bivariate ranked set sampling (BVRSS)…”

Section: Partially Rank-ordered Set (Pros)mentioning

confidence: 99%

A review of ranked set sampling and modified methods in designing control charts

Mohammadkhani

Amiri

Khoo

2023

Quality & Reliability Eng

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“…Computational and Mathematical Methods in Medicine is a doubly stochastic matrix; we model the subsetting error probabilities in the imperfect PROS as follows (see [7] and [9]):…”

Section: Partially Rank-ordered Set Samplingmentioning

confidence: 99%

“…For example, Ozturk [5] and Frey [6] have relaxed the assumption concerning the prespecification of the number of subsets in each set. Nazari et al [7] have developed nonparametric kernel density estimators using PROS data. Hatefi et al [3] have applied PROS sampling in mixture modeling to estimate the age structures of short-lived fish species.…”

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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“…Ozturk and Jafari Jozani 11 used PROS samples for estimation problems in finite population settings. Nazari et al 12 developed nonparametric kernel density estimators using PROS data. Hatefi et al 13 applied PROS sampling in the finite mixture model context to estimate the age structure of short-lived fish species using their length.…”

Section: Rank-based Sampling Designs For Binary Variablesmentioning

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

Cited by 10 publications

References 22 publications

A review of ranked set sampling and modified methods in designing control charts

A review of ranked set sampling and modified methods in designing control charts

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

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

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