Maximum likelihood inference for mixtures of skew Student-t-normal distributions through practical EM-type algorithms

Authors:
Hsiu J. Ho;Saumyadipta Pyne;Tsung I. Lin
Affiliations:
Department of Statistics, Tunghai University, Taichung, Taiwan 407;Department of Medical Oncology, Dana-Farber Cancer Institute, Harvard Medical School, Boston, USA 02115;Department of Applied Mathematics and Institute of Statistics, National Chung Hsing University, Taichung, Taiwan 404 and Department of Public Health, China Medical University, Taichung, Taiwan 404
Venue:
Statistics and Computing
Year:
2012

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Abstract

This paper deals with the problem of maximum likelihood estimation for a mixture of skew Student-t-normal distributions, which is a novel model-based tool for clustering heterogeneous (multiple groups) data in the presence of skewed and heavy-tailed outcomes. We present two analytically simple EM-type algorithms for iteratively computing the maximum likelihood estimates. The observed information matrix is derived for obtaining the asymptotic standard errors of parameter estimates. A small simulation study is conducted to demonstrate the superiority of the skew Student-t-normal distribution compared to the skew t distribution. The proposed methodology is particularly useful for analyzing multimodal asymmetric data as produced by major biotechnological platforms like flow cytometry. We provide such an application with the help of an illustrative example.