Estimating Variances of Strata in Ranked Set Sampling

• Activity Number: 339
• Type: Topic Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Min Chen and Johan Lim*+
• Companies: Yale University and Seoul National University
• Keywords: cumulative distribution function ; udgment post-stratification ; order statistics ; plug-in estimator ; population mean estimator ; variance estimation

Abstract

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.