Date of Award

5-1-2014

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Bhattacharya, Bhaskar

Abstract

When analyzing an I × J contingency table, there are situations where sampling is taken from a sampled population that differs from the target population. Clearly the resulting estimators are typically biased. In this dissertation, four adjusting methods for estimating the cell probabilities under inequality constrains, namely, raking (RAKE), maximum likelihood under random sampling (MLRS), minimum chi-squared (MCSQ), and least squares (LSQ) are developed for particular models relating the target and sampled populations. Considering the difficulty of solving primal problem due to large dimensions, we use the Khun-Tucker conditions to exploit the duality for each method. Extensive simulation is performed to provide a systematic comparison between adjusting methods. The comparisons are also made by using a measure of information loss because of biased sampling. We apply four methods to the second National Health and Nutrition Examination Survey data under reasonable constraints. Not only the performance of four methods are compared in the example, but also how different constraints affect the quality of estimation is inspected. We emphasize that a sampling is taken from a sample population that differs from a target population. In the absence of knowledge of target population, a prior distribution can be considered as describing the initial knowledge about the target population. In the dissertation we also discuss Bayesian analysis with the use of a proper prior to measure missing information.

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