Topic: Contributions to finite mixture models

Speaker: Prof. Jiahua Chen

Host: Prof. C.F. Jeff Wu

Date: Tuesday, March 4th, 2025

Time: 16:00 p.m. - 17:15 p.m.

Venue: SIN Wai Kin International Conference Centre (W201, Administration Building)

Language: Chinese

Abstract: 

Finite mixture models are formed by convex combinations of distributions from classical distribution families. They are particularly well-suited for modeling populations with homogeneous subpopulations and for accurately approximating a wide range of distributions.

However, statistical inferences concerning finite mixture models encounter numerous unexpected challenges. Given a set of independent and identically distributed observations of increasing size, consistent estimation of the mixing distribution can only be achieved at a much slower rate than usual. The likelihood function in normal mixture models is unbounded, which debilitate the maximum likelihood estimation in a general sense. Additionally, the likelihood ratio statistics for testing hypotheses regarding the number of subpopulations may diverge to infinity, instead of having the typical chi-square limiting distribution. In this presentation, we will review various advancements in the consistent estimation of mixing distributions and in testing hypotheses concerning the number of subpopulations.

Speaker Profile:

Professor Jiahua Chen, Fellow of the Royal Society of Canada (RSC) and Canada Research Chair (Tier I) in Statistics, is a faculty member in the Department of Statistics at the University of British Columbia. He has made key contributions to statistical methodology, including introducing empirical likelihood to survey sampling, inventing the EM test for finite mixture models, and developing the extended Bayesian information criterion (EBIC) for variable selection.

He is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association and has received major honors, including the Gold Medal of the Statistical Society of Canada, the CRM-SSC Prize in Statistics, and the International Chinese Statistical Association Distinguished Achievement Award.