山东大学&首都师范大学 2020年暑期统计论坛

报告题目：Conditional Test for Ultrahigh Dimensional Linear Regression Coefficients

报 告 人：崔恒建教授 （首都师范大学）

报告时间：2020年7月24日（周五） 9:00-10:00

报告地点：腾讯会议，会议ID: 165 685 652

报告摘要：

This talk 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.

欢迎各位老师同学积极参加！