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19日 14:00-15:00

报告地点：腾讯会议ID：508 126 844

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https://meeting.tencent.com/s/aVVkju4iY0QW

校内联系人：程建华 chengjh@jlu.edu.cn

报告摘要：

In this talk, we concern with a conditional test for regression coefficients in ultrahigh dimensional linear models. Conditioning on a subset of important predictors in the model, we test the overall significance of regression coefficients of the remaining ultrahigh dimensional predictors. We first propose a conditional U-statistic test (CUT) based on an estimated U-statistic for a high dimensional linear regression model and prove that its null asymptotic distribution is normal under some mild assumptions. However, the empirical power of the proposed test is inversely affected by the dimensionality of predictors. To this end, we further propose a two-stage CUT with screening (CUTS) procedure to reduce the dimensionality under the sparsity assumption and enhance the empirical power based on random data splitting strategy. In the first stage, we divide data randomly into two equal halves and apply the conditional sure independence screening to the first half to reduce the dimensionality; In the second stage, we apply the proposed CUT test to the second half. To eliminate the effect of random data splitting and further enhance the empirical power, we also develop a powerful ensemble algorithm based on multiple splitting strategy 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 test via Monte Carlo simulations and a real data analysis.

报告人简介：

崔恒建，首都师范大学教授，博士生导师，曾任国务院学位委员会学科评议组专家。研究方向主要包括数理统计和稳健统计理论及方法、金融统计、遥感统计与质量管理等，在JASA、AoS、JRSSB、Biometrika和JoE等期刊上发表论文120余篇。先后主持国家自然科学基金杰青(B)项目和4项国家自然科学基金面上项目以及青年基金项目；主要参加了国家自然科学基金重点项目、主任基金、教育部重大科研基金、科技部863计划等科研项目15余项。现担任《应用数学学报》中英文版编委、《数理统计与管理》编委、中国概率统计学会常务理事、中国现场统计学会副理事长、全国工业统计教学研究会副会长、北京应用统计学会会长、生存分析分会副理事长、国际泛华统计协会会员、美国数学会数学评论员与国际数理统计学会(中国分会)常务理事。曾获教育部高等学校科学技术奖(自然科学奖)二等奖、全国统计科学研究优秀成果奖一等奖、全国统计科学研究优秀教学成果奖二等奖、中国科协期刊优秀学术论文三等奖、北京师范大学优秀科研成果奖、国家统计局全国统计科学技术进步二等奖以及京津五四青年概率统计学术年会“盖洛普”奖等。