Type
Text
Type
Dissertation
Advisor
Nancy R. Mendell | Nancy R. Mendell. | Stephen J. Finch | Wei Zhu | Yungtai Lo.
Date
2011-08-01
Keywords
Statistics
Department
Department of Applied Mathematics and Statistics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/71639
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
Identifying the number of components in a finite mixture is hard problem. Generally, the likelihood ratio test provides a robust method for statistical inference for this problem. However, the classical theorem for the asymptotic null distribution of the LRT statistic cannot be applied to finite mixture alternatives. So other inferential methods have been proposed to assess the statistical significance of an observed LRT value. Two such methods are the bootstrap and posterior predictive check (PPC). In this dissertation we conducted simulation studies to compare the power of the bootstrap method to the PPC method as it applies to identify the number of components in a Poisson mixture. We considered two simple hypothesis tests where we test a single Poisson distribution against a mixture of two Poisson distributions and a zero inflated Poisson (ZIP) distribution. For the two-component Poisson mixture alternative, we compared the power of the PPC method to the Bootstrap method. In the case of the zero inflated Poisson (ZIP) alternative, we compared the PPC method to the bootstrap method and two asymptotic tests proposed by Rao and Chakravarti [20] and van den Broek [24] for detecting zero inflation in a Poisson. Simulated data sets were used to compare the performance of the methods for each test. A wide range of cases under these alternative hypotheses were considered with the objective of seeing whether one method is uniformly more powerful than the others for each of these alternatives.
Recommended Citation
Lee, Donghyung, "Testing for a Poisson Mixtures: Comparison of the Power of the Posterior Predictive Check (PPC) and Bootstrap Approaches" (2011). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 844.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/844