Topic: A general framework to extend sufficient dimension reductions to the cases of the mixture multivariate elliptical distributions

Time: April 2, 12:30 p.m.

Location: Tencent Conference 376419906

Moderator: Prof. Lorraine

Rapporteur Profile:

Chen Fei, Professor, Doctor of Statistics, Doctoral Supervisor, Dean of School of Statistics and Mathematics, Yunnan University of Finance and Economics. He is a reserve talent of young and middle-aged academic and technical leaders in Yunnan Province, vice president of Tourism Big Data Society of China Field Statistics Research Association, and executive director of Yunnan Provincial Applied Statistics Society. He is mainly engaged in the research in the fields of dimensionality reduction theory, statistical diagnosis, structural equation modeling, and semiparametric Bayesian theory. He has presided over 4 projects of National Natural Science Foundation of China (NSFC), and his research results were awarded the Excellent Achievement Award of Philosophy and Social Sciences of Yunnan Province.

Lecture Synopsis:

In the sufficient dimension reduction (SDR), many methods depend on some assumptions on the distribution of predictor vector, such as the linear design In the sufficient dimension reduction (SDR), many methods depend on some assumptions on the distribution of predictor vector, such as the linear design condition (L.D.C.), the assumption of constant conditional variance, and so on. In this article, a general framework is proposed to extend various SDR methods to the cases where the predictor vector follows the mixture elliptical distributions. follows the mixture elliptical distributions, together with the asymptotic property for the consistency of the kernel matrix estimators. For illustration, the extensions of several SDR methods are used. illustration, the extensions of several classical SDR approaches under the proposed framework are detailed. Moreover, a method to estimate the structural dimension is given, together with the asymptotic property for the consistency of the kernel matrix estimators. Moreover, a method to estimate the structural dimension is given, together with a procedure to check an assumption called homogeneity. The proposed methodology is illustrated by simulated and real examples.