题目：Conditional Test for Ultrahigh Dimensional Linear Regression Coefficients

报告人：钟威

时间：2020年11月6日 10：00-11：00

地点：腾讯会议 ID 100 190 344

摘要：This paper is concerned with a conditional test for the overall significance of regression coefficients in ultrahigh dimensional linear models conditional on a subset of predictors. We first propose a conditional U-statistic test (CUT) based on an estimated U-statistic for a moderately high dimensional linear regression model and derive its asymptotic distributions under some mild assumptions. However, the empirical power of the CUT test is inversely affected by the dimensionality of predictors. To this end, we further propose a two-stage CUT with screening (CUTS) procedure based on random data splitting strategy to enhance the empirical power . In the first stage, we divide data randomly into two parts and apply the conditional sure independence screening to the first part to reduce the dimensionality; In the second stage, we apply the CUT test to the reduced model using the second part of the data. To eliminate the effect of data splitting randomness and further enhance the empirical power, we also develop a powerful ensemble CUTS_M algorithm based on multiple data splitting and prove that the family-wise error rate is asymptotically controlled at a given significance level. We demonstrate the excellent finite-sample performances of the proposed conditional tests via Monte Carlo simulations and two real data analysis examples.

简介：钟威，现任厦门大学王亚南经济研究院和经济学院统计系教授、博士生导师，经济学院院长助理。2012年获得美国宾夕法尼亚州立大学统计学博士学位，2014年和2017年分别破格晋升副教授和教授，2018年入选厦门大学“南强青年拔尖人才”（A类），国家自然科学基金优秀青年基金获得者（2019），福建省杰出青年基金获得者（2019）。主要从事高维数据统计分析和理论、统计学习和数据挖掘算法、计量经济学内生问题、统计学和数据科学的应用等领域的研究。担任美国统计协会(ASA)统计学和数据科学期刊《Statistical Analysis and Data Mining》的AE，在The Annals of Statistics, Journal of the American Statistical Association, Biometrika, Journal of Business & Economic Statistics, Annals of Applied Statistics,  Statistica Sinica，中国科学数学等国内外统计学权威期刊发表（含接收）20多篇论文。