报告题目：Integrated conditional moment test and beyond: when the number of covariates is divergent
报告人：朱力行 教授
报告时间：2021年6月2日(星期三)14:00-15:00
腾讯会议ID：906 192 397或点击链接：
https://meeting.tencent.com/s/HZy1TPG4UIha
线下会议地点：藕舫楼629
主持人：曹春正 教授
报告内容简介：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.
报告人简介：朱力行教授，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，香港浸会大学讲座教授，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；分别于1989年，2014年获国家教委科学技术进步二等奖和中国教育部自然科学奖二等奖；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。
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数学与统计学院
江苏省统计科学研究基地
2021年6月1日