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Degree

Doctor of Philosophy, Ohio State University, Statistics, 2005.

Abstract

Ranked set sampling (RSS) is a sampling scheme which can successfully replace simple random sampling (SRS) in experimental settings where measuring the units of interest is difficult, expensive, or time consuming, but ranking small subsets of units is relatively easy and inexpensive. Under perfect ranking, the statistical inference based on a RSS data is more efficient than the inference based on a SRS data of equal size. In practice, the ranking process is most likely subject to errors, and the efficiency of the inference decreases with the decrease in the quality of the ranking procedure. Thus, the central issue of a parametric inference is to balance the two ideals: efficiency when the ranking is perfect, and robustness when the ranking is imperfect. Typically there is a trade-off between these two ideals. In order to address this issue, we develop robust statistical inference based on a RSS data from a family of discrete distributions. Our inference relies on minimum disparity functions that measure the distance between the empirical and model distributions. We develop a class of estimators obtained by minimizing disparities between the assumed and empirical models. We show that all minimum disparity estimators are asymptotically efficient at the correct model under perfect ranking. We also show that there exists an estimator within this class, the minimum Hellinger distance estimator, that produces substantially smaller bias than the bias of the maximum likelihood estimator under imperfect ranking. In addition to robust estimation, we also developed a class of testing procedures, referred to as disparity deviance tests, to test certain hypotheses about the parameters of a family of discrete distributions. We show that under perfect ranking, the disparity deviance tests have the same asymptotic null distribution as the likelihood ratio test. Furthermore, we show that the disparity deviance test based on the Hellinger distance is more stable to imperfect ranking than the likelihood ratio test. We provide finite sample simulation results to evaluate the performance of the proposed procedures.

Subject Headings

Statistics

Keywords

Bias; Mean square error; Hellinger distance; Imperfect ranking; Robustness; Minimum distance estimation

Advisor

Omer Ozturk

Document number: osu1126033164
Permalink: http://rave.ohiolink.edu/etdc/view?acc_num=osu1126033164

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