线上学术报告

Title: A kernel-based measure for conditional mean dependence

Speaker: 张忠占教授（北京工业大学理学部）

Abstract

We propose a novel metric, called kernel-based conditional mean dependence (KCMD), to measure and test departure from conditional mean independence between a response variable Y and a predictor variable X, where X and Y can be vector-valued or function-valued, based on the reproducing kernel embedding and Hilbert-Schmidt norm of a tensor operator. The kernel-based conditional mean dependence has several appealing merits. It equals zero if and only if the conditional mean of Y given X is independent of X, i.e. E(Y|X)=E(Y) almost surely, provided that the chosen kernel is characteristic; it does not involve any tuning parameters when used to functional data; it can be used to detect the nonlinear conditional mean dependence with an appropriate choice of the kernel according to the feature of the studying data. We define a U-statistic estimator of KCMD and present a wild bootstrap test to the conditional mean independence. The limit distributions of the test statistic and the bootstrapped statistics under null hypothesis, fixed alternative hypothesis and local alternative hypothesis are given, and a data-driven procedure to choose a suitable kernel is suggested. Simulation studies indicate that the tests based on the KCMD have close powers to tests based on martingale difference divergence in monotone relationships, but excel in nonlinear relationships and relationships that the moment restriction on X is violated. Also, a real data example of using this testing procedure is presented.

报告人简介：张忠占，北京工业大学教授，博士生导师，中国现场统计研究会副理事长兼秘书长，国际生物统计学会中国分会副理事长，国家药监局医疗器械临床试验专家组专家。1999年于日本九州大学获得博士学位。主要研究方向：函数型数据分析，生物统计。历任北京工业大学应用数理学院院长，研究生院常务副院长；中国科协第八、九届全国委员会委员，曾任中国现场统计研究会副理事长兼生物统计分会理事长，教育部统计学专业教学指导委员会委员，国家统计局专家委员会委员等。担任《数理统计与管理》副主编，《International Journal of Biomathematics》Editor。

北京时间：2022年6月9日（周四）下午16:00-17:00

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