JSM 2004 - Toronto

Abstract #301893

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Activity Number: 180
Type: Topic Contributed
Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
Sponsor: General Methodology
Abstract - #301893
Title: Unbalanced Ranked Set Sampling for Estimating a Population Proportion
Author(s): Haiying Chen*+ and Elizabeth A. Stasny and Douglas Wolfe
Companies: Ohio State University and Ohio State University and Ohio State University
Address: 1958 Neil Ave., Columbus, OH, 43210,
Keywords: binary variable ; Neyman allocation ; perfect ranking ; relative precision
Abstract:

Application of ranked set sampling (RSS) techniques to data from a dichotomous population has been an active research topic recently. It has been shown that balanced RSS leads to improvement in precision over simple random sampling (SRS) for estimation of a population proportion. Balanced RSS, however, is not optimal in terms of variance reduction for this setting. The objective of this paper is to investigate the application of unbalanced RSS to estimation of a population proportion under perfect ranking, where the probabilities of success for the order statistics are functions of the underlying population proportion. In particular, Neyman allocation, which assigns sample units for each order statistic proportionally to its standard deviation, is shown to be optimal in the sense that it leads to minimal variance within the class of RSS estimators that are unweighted averages of the order statistics. We also use a substantial dataset, the NHANES III data to demonstrate the feasibility and benefits of Neyman allocation in RSS for binary variables.

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