Efficiency comparisons for partially rank-ordered set sampling
type: Item
instance of: scholarly article
title: Efficiency comparisons for partially rank-ordered set sampling
zbMATH Open document ID: 1387.62067
author: Timothy G. Feeman
author: Jesse Frey
published in: Statistical Papers
publication date: 2017-12-13T00:00:00Z
review text: Choose a set size \(m\). Draw \(M\) independent samples (sets) of size \(m\) and rank the units in each set, where ranking is by judgment or by using a covariate. A sample for measurement then consists of the smallest ranked unit in the first set, the second smallest ranked in the second set, and so on\dots This will be a balanced ranked-set sample. We shall now describe a balanced partially rank-ordered set sample (PROSS). Consider a vector of subset sizes \((m_1,m_2,\dots,m_M)\) with a total set size \(m=\sum^M_{i=1}m_i\). Draw \(m\) independent sets of size \(m\) and divide the units in each set into \(M\) ordered subsets of sizes \((m_1,m_2,\dots,m_M)\) such that for \(1\leq i\leq j\leq M\), all units in the \(i\)th subset are ranked smaller than all the units in the \(j\)th subset. Next, a sample for measurement is obtained by selecting one unit drawn at random from the first subset in each of the first \(m_1\) sets, one unit drawn at random from the second subset in each of the \(m_2\) sets, and so on. This gives a sample of \(m\) independent values, with \(m_i\) values coming from the \(i\)th subset in their set of size \(m\). It may be noted that the PROSS scheme \((1,1,\dots 1)\) where there are \(m\) subsets each of size 1 corresponds to balanced RSS with set size \(m\). In this paper, the authors study the efficiency of PROSS sample mean under perfect rankings for various such PROSS schemes. They show that PROSS \((km_1,km_2,\dots,km_M)\) is always more efficient than the scheme \((m_1,m_2,\dots,m_M)\) for \(k>1\). Furthermore, they give a comparison of two PROSS schemes in the two subset case. Finally, Ozturk's conjecture that PROSS with \(m\) subsets of size \(k>1\) is always more efficient than RSS with set size \(m\) is proved as a corollary to a more general result which uses majorization.
reviewed by: T. J. Rao
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 62D05
zbMATH DE Number: 6818220
zbMATH Keywords: majorization
zbMATH Keywords: order statistics
zbMATH Keywords: perfect rankings
zbMATH Keywords: ranked-set sampling
MaRDI profile type: Publication
full work available at URL: s00362-016-0742-2
OpenAlex ID: W2301573885
cites work: Estimation of the shape and scale parameters of Pareto distribution using ranked set sampling
cites work: Modified inference about the mean of the exponential distribution using moving extreme ranked set sampling
cites work: Majorization: here, there and everywhere
cites work: Order Statistics
cites work: Efficiency bounds for a generalization of ranked-set sampling
cites work: Distribution-free statistical intervals via ranked-set sampling
cites work: Two sample distribution-free inference based on partially rank-ordered set samples
cites work: Q5344608
cites work: Group sequential methods based on ranked set samples
cites work: Unbiased and almost unbiased ratio estimators of the population mean in ranked set sampling
cites work: Ratio estimator for the population mean using ranked set sampling
cites work: Rounded data analysis based on ranked set sample
cites work: A New Ranked Set Sample Estimator of Variance
cites work: Inequalities: theory of majorization and its applications
cites work: Quantile inference based on partially rank-ordered set samples
cites work: Some Relations Between Expectations of Order Statistics in Samples of Different Sizes
cites work: Parametric ranked set sampling
cites work: Characterization of a Ranked-Set Sample with Application to Estimating Distribution Functions
cites work: On unbiased estimates of the population mean based on the sample stratified by means of ordering
DOI: 10.1007/S00362-016-0742-2
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description: scientific article; zbMATH DE number 6818220