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：2020.12.01 上午9:30 – 11:30

报告地点：数理楼145报告厅

摘要: The classic integrated conditional moment (ICM) test is a promising method for model checking and its basic idea has been applied to develop several variants. However, in diverging dimension scenarios, the ICM test may break down and has completely different limiting properties from those in fixed dimension cases, and the related wild bootstrap approximation would also be invalid. To extend the ICM test to diverging dimension settings, we propose a projected adaptive-to-model version of the ICM test. We study the asymptotic properties of the new test under both the null and alternative hypotheses 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 rate n^−1/2 .The wild bootstrap can still work for the new test in diverging dimension scenarios. We also derive 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. The numerical studies show that the new test can greatly enhance the performance of the ICM test in high-dimensional cases. We also apply the test to a real data set for illustrations.

简介：谭发龙，湖南大学金融与统计学院助理教授，香港浸会大学统计学博士。主要研究方向为高维假设检验、充分降维、经验过程等，研究成果发表在The Annals of Statistics，Statistica Sinica等期刊。