学术报告
Approximately Oracle Generalized Likelihood Ratio Test for High-dimensional Linear Regression - 蒋学军（南方科技大学统计与数据科学系）
“2021首师大青年统计论坛”系列报告
题目：Approximately Oracle Generalized Likelihood Ratio Test for High-dimensional Linear Regression
报告人：蒋学军（南方科技大学统计与数据科学系）
时间：2021年4月22日周四晚上19:00-20:00
地点：线上腾讯会议（会议号：709 455 5647）
Abstract : In this paper we propose an approximately oracle test (AOT) to test linear hypotheses in high dimensional linear models. To deal with linear hypotheses test, we first investigate the difficulty in using the ordinary least square estimation in high-dimensional regression and then propose a projection least square estimation (PLSE) to surmount it. The PLSE is essentially an ordinary LSE based on the reduced feature space. Based on the PLSE, we propose the generalized likelihood ratio (GLR), Wald(G-W) and Score (G-S) statistics and give the uniform closed expression for the above three statistics. However, the GLR, G-W and G-S depend on a random feature space, unless the reduced feature space is the true feature space. To deal with the random feature space, we propose the refitted test statistic (R-TS) based on the uniform closed expression. We establish asymptotic null and alternative distributions of the R-TS. It demonstrates that the Wilks' type of results still hold in the high dimensional setting. Simulations are conducted to examine finite sample performance of the proposed test. A real example illustrates the use of our proposed testing procedure.
报告人简介：蒋学军，现任南方科技大学统计与数据科学系长聘副教授、博士生导师。2006年硕士毕业于云南大学统计系，2009年于香港中文大学获得博士学位，09-10（2010/09-2010/09）在港中文从事博士后研究工作，2013年07月加入南方科技大学，入选深圳市海外高层次人才孔雀计划(2016)，深圳市优秀教师(2018)，主持有国家自然科学基金（青年，面上）、广东省自然科学面上基金(2项)、深圳市科创委基础研究项目、深圳市技术委托开发项目、及广东省教学改革项目等。主要研究方向包括金融统计与计量、分位数回归、变量选择、高维统计推断、及贝叶斯应用等。已在统计学主流期刊和相关金融、经济等交叉学科期刊上发表SCI&SSCI论文45余篇，出版英文教材一部。
联系人：周洁、胡涛
举办单位：77779193永利官网统计系 、北京应用统计学会、交叉科学研究院
