Mixture Models

Dr. Weixin Yao is professor and vice chair of the Department of Statistics at the University of California, Riverside. He received his BS in statistics from the University of Science and Technology of China in 2002 and his PhD in statistics from Pennsylvania State University in 2007. His major research includes mixture models, nonparametric and semiparametric modeling, robust data analysis, and high-dimensional modeling. He has served as an associate editor for Biometrics, Journal of Computational and Graphical Statistics, Journal of Multivariate Analysis, and The American Statistician. In addition, Dr. Yao was also the guest editor of Advances in Data Analysis and Classification for the special issue on “Models and Learning for Clustering and Classification," 2020-2021.Dr. Sijia Xiang is a professor in statistics. She obtained her doctoral and master's degrees in statistics from Kansas State University in 2014 and 2012, respectively. Her research interests include mixture models, nonparametric/semiparametric estimation, robust estimation, and dimension reduction. Dr. Xiang has led several research projects, including, "Statistical inference for clustering analysis based on high-dimensional mixture models," funded by the National Social Science Fund of China, "Semiparametric mixture model and variable selection research," funded by the National Natural Science Foundation of China, and "Research on the new estimation method and application of mixture model," funded by the Zhejiang Statistical Research Project. Dr. Xiang has also been selected as a Young Discipline Leader and a Young Talented Person in the Zhejiang Provincial University Leadership Program.Dr. Xiang has published extensively in international journals, including Annals of the Institute of Statistical Mathematics, Statistical Science, Journal of Statistical Planning and Inference, and more. Her research mainly focuses on semiparametric mixture models, which include semiparametric mixtures of regressions with single-index for model-based clustering, semiparametric mixtures of nonparametric regressions, and continuous scale mixture approaches. Dr. Xiang has also contributed to the development of new estimation methods for mixtures of linear regression models and mixtures of factor analyzers. Additionally, she has proposed a new bandwidth selection method for nonparametric regressions and robust maximum Lq-likelihood estimation for joint mean-covariance models for longitudinal data.

• 1. 1. Introduction to Mixture Models. 2. Mixture models for discrete data. 3. Mixture regression models. 4. Bayesian mixture models. 5. Label switching for mixture models. 6. Hypothesis testing and model selection for mixture models. 7. Robust mixture regression models. 8. Mixture models for high dimensional data. 9. Semiparametric mixture models. 10. Semiparametric mixture regression models.

"Across 380 pages, it covers most aspects of mixture (and hidden Markov) estimation with strong emphasis on maximum likelihood estimation, while the new directions are unsurprisingly those pursued by the authors, namely robust and semiparametric estimation, as well as model selection by testing.~Christian Robert (Column Editor) (2024),CHANCE, 37:4, 60-61