报告题目: Integrated conditional moment test and beyond: when the number of covariates is divergent
报 告 人: 朱力行（香港浸会大学首席教授）
报告时间: 2020年9月23日(周三)， 14：30-15：30
腾讯会议https://meeting.tencent.com/s/bYAj47krvMGF
会议ID：366 823 552
报告摘要：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.
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科学技术处
2020年9月21日