报告题目：Integrated Conditional Moment Test and Beyond: When the Number of Covariates is Divergent

主 讲 人：朱力行

单 位：北京师范大学

时 间：5月14日9:30

腾 讯 ID：409 529 233

地 点：学院二楼会议室

摘 要：

The classic integrated conditional moment test is a proven promising method for testing model misspecification. However, in diverging dimensionality scenarios, our study in this paper shows the failures of this test and the related wild bootstrap approximation because of completely different limiting properties from those in fixed dimension cases. To extend it to handle the testing problem with diverging number of covariates, we investigate three issues in inference in this paper. First, we study the consistency and asymptotically linear representation of the least squares estimator of the parameter at the fastest rate of divergence in the literature for nonlinear models. Second, we propose a projected adaptive-to-model version of the integrated conditional moment test. We study the asymptotic properties of the new test under both the null and alternative hypothesis to examine its ability of significance level maintenance and its sensitivity to the global and local alternatives that are distinct from the null at the fastest possible rate in hypothesis testing. Third, we derive the consistency of the wild bootstrap approximation for the null distribution in the diverging dimension setting. The numerical studies show that the new test can very much enhance the performance of the original ICM test in high-dimensional cases. We also apply the test to a real data set for illustrations.

简 介：

朱力行，北京师范大学统计与数据科学研究中心首席专家，北京师范大学统计学院教授委员会主席。美国科学促进会(AAAS)，美国统计学会(ASA)，以及美国数理统计研究院(IMS) fellow和国际统计研究院(ISI) elected member。1989年，2014年获国家教委科学技术进步奖二等奖和中国教育部自然科学奖二等奖；获2013年度国家自然科学奖二等奖（独立获奖人）。1998年获德国洪堡研究奖（中国自然科学领域第一位获奖者，亚洲统计学界唯一获奖者）；1997年获国家基金委杰出青年基金，1999年获中国科学院百人计划支持。2004年-2007年任中国人民大学长江讲座教授。