Mixture modeling has numerous applications. One particular interest is microarray data analysis. My dissertation research is focused on the Contaminated Chi-Square (CCS) Modeling and its application in microarray. A moment-based method and two likelihood-based methods including Modified Likelihood Ratio Test (MLRT) and Expectation-Maximization (EM) Test are developed for testing the omnibus null hypothesis of no contamination of a central chi-square distribution by a non-central Chi-Square distribution. When the omnibus null hypothesis is rejected, we further developed the moment-based test and the EM test for testing an extra component to the Contaminated Chi-Square (CCS+EC) Model. The moment-based approach is easy and there is no need for re-sampling or random field theory to obtain critical values. When the statistical models are complicated such as large mixtures of dimensional distributions, MLRT and EM test may have better power than moment based approaches, and the MLRT and EM tests developed herein enjoy an elegant asymptotic theory.
| Identifer | oai:union.ndltd.org:uky.edu/oai:uknowledge.uky.edu:statistics_etds-1009 |
| Date | 01 January 2014 |
| Creators | Zhou, Feng |
| Publisher | UKnowledge |
| Source Sets | University of Kentucky |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Theses and Dissertations--Statistics |
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