数学与统计学院学术报告[2019] 113号

(高水平大学建设系列报告344号)

报告题目: Integrated conditional moment test and beyond: when the number of covariates is divergent  

报告人：  谭发龙 助理教授  （湖南大学）

报告时间：2019年12月6日16:00—17:00

报告地点： 汇星楼501

报告内容：

   The classic integrated conditional moment test is a promising method for testing model misspecification. However, it severely suffers from the curse of dimensionality. 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 in the diverging scenarios. 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 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.  

报告人简历：

   谭发龙2017年在香港浸会大学获得博士学位，现任湖南大学金融与统计学院助理教授，主要研究兴趣包括高维经验过程、高维假设检验、充分降维等，相关研究成果发表在Annals of Statistics和Statistica Sinica等国际期刊上。

   欢迎感兴趣的师生参加！

数学与统计学院

2019年12月2日