Hypothesis testing on the number of components in finite mixture models Open Access

Zhang, Mingrui (Spring 2020)

Permanent URL: https://etd.library.emory.edu/concern/etds/sb3979381?locale=en


In this paper, we develop a mathematical framework for studying finite mixture models based on a quotient space, a parameter space viewing parameterizations corresponding to same probability distribution as same equivalence class. The quotient space is used to solve the issue of identifiability in finite mixture models, which makes the study of asymptotic properties of maximum likelihood estimation (MLE) possible. In the quotient space, we prove the consistency of MLE under some conditions and use simulation designs to show the performance of the point estimation of parameters by EM algorithm. Also, we propose a generalized Wald test based on resampling. By simulation studies, we show that our generalized Wald tests under two-component Gaussian mixture models may be more powerful than the likelihood ratio tests in many cases. 

Table of Contents

1 Introduction 1

2 Method 2

2.1 Finite mixture models 2

2.2 Hypothesis test 3

2.3 Computation 5

3 Study on Gaussian mixture models 6

3.1 Evaluation of point estimation by EM algorithm 6

3.2 Simulation study on the power of hypothesis testing 7

4 Discussion 7

References 8

Appendix A Proof of Proposition 1-2 11

Appendix B Tables and Figures 18

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