Linear hypothesis testing for high dimensional generalized linear models

报告人：李润泽
报告地点：数学与统计学院415室
报告时间：2018年10月09日星期二16:00-17:00
报告摘要：

This paper is concerned with testing linear hypotheses in high-dimensional generalized linear models. To deal with linear hypotheses, we first propose constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are $\chi^2$ distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow non-central $\chi^2$ distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to $\infty$ at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures.

主讲人简介：
李润泽教授是美国宾夕法尼亚州立大学统计系冠名讲座教授，国际最权威统计学学会Institute of Mathematical Statistics和American Statistical Association的Fellow。曾任世界顶级统计学刊物The Annals of Statistics的联合主编。李润泽教授在高维数据变量选择、超高维数据特征提取、纵向数据分析、以及统计遗传学和生物信息学等方面都做了很多重要的工作。李教授学术成果卓越，已在统计学四大国际顶级期刊Annals of Statistics, JASA, JRSSB, Biometrika上发表30余篇文章并多次入选“高被引（亦被称为世界顶尖）科学家”。