报告题目:Test and Measure for Partial Mean Dependence Based on Machine Learning Methods
时间:2023年9月28日(星期四)下午14:00-15:00
地点:沙河校区,二教205
报告人:郭旭,北京师范大学统计学院,教授
摘要:It is of importance to investigate the significance of a subset of covariates $W$ for the response $Y$ given covariates $Z$ in regression modeling. To this end, we propose a significance test for the partial mean independence problem based on machine learning methods and data splitting. The test statistic converges to the standard chi-squared distribution under the null hypothesis while it converges to a normal distribution under the fixed alternative hypothesis. Power enhancement and algorithm stability are also discussed. If the null hypothesis is rejected, we propose a partial Generalized Measure of Correlation (pGMC) to measure the partial mean dependence of $Y$ given $W$ after controlling for the nonlinear effect of $Z$. We present the appealing theoretical properties of the pGMC and establish the asymptotic normality of its estimator with the optimal root-$N$ convergence rate. Furthermore, the valid confidence interval for the pGMC is also derived. As an important special case when there are no conditional covariates $Z$, we introduce a new test of overall significance of covariates for the response in a model-free setting. Numerical studies and real data analysis are also conducted to compare with existing approaches and to demonstrate the validity and flexibility of our proposed procedures.
报告人简介:郭旭,北京师范大学统计学院教授,博士生导师。郭老师一直从事回归分析中复杂假设检验的理论方法及应用研究,近年来皆在对高维数据发展适当有效的检验方法。部分成果发表在JRSSB, JASA,Biometrika和JOE。担任《应用概率统计》杂志第十届编委。现主持国家自然科学基金优秀青年基金。曾荣获北师大第十一届“最受本科生欢迎的十佳教师”和北师大第十八届青教赛一等奖。
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