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Abstract Details

Activity Number: 339
Type: Topic Contributed
Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #307721
Title: Estimating Variances of Strata in Ranked Set Sampling
Author(s): Min Chen and Johan Lim*+
Companies: Yale University and Seoul National University
Address: Department of Statistics,, Seoul, 151-747, South Korea
Keywords: cumulative distribution function ; udgment post-stratification ; order statistics ; plug-in estimator ; population mean estimator ; variance estimation

In the ranked set sampling, the variance of observations in each ranked set plays an important role in finding an optimal design for unbalanced RSS and in inferring the population mean. The empirical estimator is most commonly used for estimating the variance in the literature. However, the empirical estimator does not use the information in the entire data over different ranks. Further, it is highly variable when the sample size is not large enough, as is typical in RSS applications. In this paper, we propose a plug-in estimator for the variance of each stratum, which is more efficient than the empirical one. We analytically prove the asymptotic normality of the proposed estimator. We further apply it to estimate the standard error of the RSS mean estimator. Both our simulation and empirical study show that our estimators consistently outperform existing methods.

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