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Homogeneity test in finite mixture models using EMtest Open Access
Descriptions
 Other title
 Subject/Keyword

EMtest
multivariate mixture model
scale mixture of normal model
contaminated normal model
mixture model
homogeneity test
 Type of item
 Thesis
 Degree grantor

University of Alberta
 Author or creator

Niu, Xiaoqing
 Supervisor and department

Li, Pengfei (Department of Statistics and Actuarial Science; University of Waterloo)
Mizera, Ivan (Department of Mathematical and Statistical Sciences)
 Examining committee member and department

Karunamuni, Rohana (Department of Mathematical and Statistical Sciences)
Charnigo, Richard (Department of Biostatistics, Department of Statistics; University of Kentucky)
Wang, Zhiquan (Agricultural, Food & Nutritional Science)
 Department

Department of Mathematical and Statistical Sciences
 Specialization

Statistics
 Date accepted

20131204T16:10:03Z
 Graduation date

201406
 Degree

Doctor of Philosophy
 Degree level

Doctoral
 Abstract

The class of finite mixture models is widely used in many areas, including science, humanities, medicine, engineering, among many others. Testing homogeneity is one of the important and challenging problems in the application of finite mixture models. It has been investigated by many researchers and most of the existing works have focused on the univariate mixture models, normal mixture models on the mean parameters only, and normal mixture models on both mean and variance parameters. This thesis concentrates on testing homogeneity in multivariate mixture models, scale mixtures of normal distributions, and a class of contaminated normal models. We first propose the use of the EMtest (Li, Chen, & Marriott, 2009) to test homogeneity in multivariate mixture models. We show that the EMtest statistic has asymptotically the same distribution as the likelihood ratio test for testing the restricted mean of a multivariate normal distribution given one observation. Based on this result, we suggest a resampling procedure to approximate the pvalue of the EMtest. Scale mixture of normal distributions, i.e., mixture of normal distributions on the variance parameters, has wide applications. However, an effective testing procedure speciﬁcally for testing homogeneity in this class of mixture models is not available. We retool the EMtest (Chen & Li, 2009) for testing homogeneity in the scale mixture of normal distributions. We show that the retooled EMtest has the simple limiting distribution $\frac{1}{2} \chi^2_0 + \frac{1}{2}\chi^2_1$. Largescale hypothesis testing problem appears in many areas such as microarray studies. We propose a new class of contaminated normal models, which is a twocomponent normal mixture model with one component mean being zero and different component variances, and can be used in largescale hypotheses. We further design a new EMtest for testing homogeneity in this class of mixture models. It is shown that the new EMtest statistic has a simple shifted $\frac{1}{2} \chi^2_1 + \frac{1}{2}\chi^2_2$ limiting distribution. In all the three scenarios, extensive simulation studies are conducted to examine whether the limiting distributions approximate the finite sample distributions reasonably well and whether the EMtests have appropriate power to detect heterogeneity in the alternative models. To demonstrate the application of the proposed methods, several realdata examples are analyzed.
 Language

English
 DOI

doi:10.7939/R3X63BC3Z
 Rights
 This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
 Citation for previous publication

Niu, Xiaoqing, Pengfei Li, and Peng Zhang. "Testing homogeneity in a multivariate mixture model." Canadian Journal of Statistics 39.2 (2011): 218238.
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File title: Introduction
File title: Homogeneity Test In Finite Mixture Models Using EMtest
File author: Xiaoqing Niu
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