【报告摘要】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.

【报告人简介】Dr. Jiahua Chen earned his Bachelor’s degree from the University of Science and Technology of China in 1982, followed by a Master’s degree from the Institute of Systems Science at Academia Sinica in January 1985 under the guidance of Professor Ping Cheng. He went on to complete his Ph.D. at the University of Wisconsin-Madison in July 1990, under the supervision of Professor Jeff Wu.

Dr. Jiahua Chen began his academic journey at the Department of Statistics and Actuarial Science at the University of Waterloo as a visiting scholar in 1989. He then pursued a one-year postdoctoral appointment under the supervision of Professor John D. Kalbfleisch. Subsequently, he accepted an assistant professorship in 1991 and was steadily promoted to associate and full professor.

In January 2007, Dr. Chen transitioned to the Department of Statistics at the University of British Columbia, where he held the prestigious Canada Research Chair, Tier I position until December 2020. He continues to serve as a full professor at UBC. Initially focusing on problems in experimental design, his research interests quickly expanded to encompass Finite Mixture Models, Empirical Likelihood, Survey Methodology, and other areas.

Dr. Jiahua Chen takes pride in several notable contributions to the field, including his work on the periodicity of minimum aberration fractional factorial designs, insights into the optimal convergence rate for estimating mixing distributions, development of the EM-test for the order of finite mixture models, pioneering research on nearest neighbor imputation in sampling data analysis, introduction of empirical likelihood to sampling problems, and invention of the extended Bayesian information criterion for large model spaces.

Recognized for his exceptional achievements, Dr. Chen is an elected fellow of both the Institute of Mathematical Statistics and the American Statistical Association. He has been honoured with the prestigious CRM-SSC Prize in Statistics for his outstanding contributions to the statistical sciences. Additionally, he received the Gold Medal, the highest honour bestowed by the Statistical Society of Canada, in 2014, and the Distinguished Achievement Award from the International Chinese Statistical Association in 2016. In 2022, he was elected as a fellow of the Royal Society of Canada.