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Degree

Doctor of Philosophy, Ohio State University, Statistics, 2008.

Abstract

Ranked set sampling (RSS) is a method of data collection that makes use of the sampler's judgment of relative sizes of potential sample units. In RSS, the observations quantified by the researcher generally will be more representative of the range of values in the population than those obtained from simple random sampling (SRS). RSS has been shown to result in more precise estimators than SRS. Although there is a growing body of research on RSS, the area is unfamiliar to most sampling statisticians. In this dissertation, we demonstrate how RSS can be utilized in survey sampling settings. We begin by exploring the feasibility of incorporating RSS into a stratified sampling design. We call this technique stratified ranked set sampling (SRSS). In addition to its value as a sampling device, stratified sampling forms the theoretical basis of more complex sampling designs. By exploring RSS in stratified sampling first, we are laying the foundations for further research on how RSS can be incorporated into methodologies commonly used by survey samplers. We develop the theory of how to construct confidence intervals for the estimator of the mean under SRSS. Our simulations show that in most circumstances these confidence intervals are shorter than those under stratified SRS. We describe methods to search for the best way to allocate observations to the strata and ranks under SRSS. The number of possible allocations is extremely large, even for nominally small problems. This precludes an exhaustive search, so we turn our attention to methods that search subsets of the allocation space. Simulated annealing is an attractive method because it is easy to program and computationally efficient. When the optimal allocation assigns zero observations to a particular rank, the resultant estimator may be horribly biased. We investigate two methods to deal with this problem. We digress from SRSS at the end of this dissertation to discuss ratio estimation under RSS. Ratio estimation is another method that is commonly used in survey sampling. We provide some insight into the best selection of variables to use in RSS ratio estimation if one wants to minimize the MSE of the estimator.

Subject Headings

Statistics

Keywords

Stratified sampling; Ratio estimation; Sample allocation; Simulated annealing

Committee / Advisors

Elizabeth A. Stasny, PhD (Advisor)
Douglas A. Wolfe, PhD (Advisor)
Steven N. MacEachern, PhD (Committee Member)

Pages

163p.

Document number: osu1218543909
Permalink: http://rave.ohiolink.edu/etdc/view?acc_num=osu1218543909

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