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讲座主题：Integrated conditional moment test and beyond: when the number of covariates is divergent
主讲人： 朱力行教授 北京师范大学
讲座时间：2020/9/27 16:00-18:00
参与方式：点击链接入会，或添加至会议列表：
https://meeting.tencent.com/s/USymBxRBFyLk
会议 ID：362 878 228
会议直播: https://meeting.tencent.com/l/nAHdJ64IJHQJ
主讲人简介：
朱力行，1990年在中国科学院获得理学博士，1993年在中国科学院应用数学所评为研究员/博士导师。现在是北京师范大学太阳成集团tyc7111cc教授。1998年获得德国洪堡研究奖，是自然科学，工程，医学领域中，大陆，香港，台湾，澳门第一位获奖者，迄今为止，还是亚洲统计学界唯一获奖者。2003年，2007年和2016年分别当选为美国数理统计研究院fellow,美国统计协会fellow和美国科学促进会fellow. 2013年独立获得中国国家自然科学奖二等奖。1997年获得高层次青年基金资助，1999年入选中科院百人计划。

讲座摘要：
The classic integrated conditional moment (ICM) test is a proven promising method for testing model misspecification for fixed dimension paradigms. However, in diverging dimension scenarios, our study in this paper shows the failures of this test and the related wild bootstrap approximation to maintain the significance level and keep reasonable powers because of completely different limiting properties from those in fixed dimension cases. To extend the ICM test to handle the testing problem with diverging number of covariates, we investigate three issues in inference in this paper. First, under both the null and alternative hypothesis, 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 such that its availability for approximating the null distribution of the test 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.