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.
报告人简介：
崔恒建现为首都师范大学教授，博士生导师，曾任国务院学位委员会学科评议组专家。1993 年毕业于中国科学院系统科学研究所并获得博士学位。在数理统计和稳健统计理论和方法、金融统计、遥感统计与质量管理等领域取得过许多重要的研究成果，发表论文 180 余篇，其中包括发表在国际顶级的统计和计量经济学杂志JASA、AoS、JRSS(B)、Biometrika 和 JoE 上。多次赴美国、加拿大、意大利、新加坡、澳大利亚和香港等著名大学进行学术合作研究。主持了国家自然科学基金杰青（B）项目和多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、主任基金项目，教育部重大科研基金项目，科技部863 等项目。现担任《数学学报》和《应用数学学报》中、英文版以及《Statistical Theory and Related Fields》编委，中国现场统计学会副理事长，北京应用统计学会会长，国际数理统计学会（中国分会）常务理事。曾获得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质成果一等奖；京津地区五四青年概率统计“盖洛普”奖；第六届中国科协期刊优秀论文奖；全国应用统计专业硕士案例大赛一等奖等。
欢迎各位老师同学积极参加！
