讲座题目：条件期望独立性检验

时间：2023年06月16日（周五）上午09:00-11:30

地点：理学楼A301

报告人：张忠占教授

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。从事数理统计及其应用研究，包括函数型数据分析，生物统计，可靠性统计分析。曾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。担任《数理统计与管理》副主编，《International Journal of Biomathematics》编委（Editor）。

讲座内容：

A novel metric, called kernel-based conditional mean dependence (KCMD), is proposed to measure and test the departure from conditional mean independence between a response variable Y and a predictor variable X, based on the reproducing kernel embedding and the Hilbert-Schmidt norm of a tensor operator. The KCMD 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 employed kernel is characteristic; it can be used to detect all kinds of conditional mean dependence with an appropriate choice of kernel; it has a simple expectation form and allows an unbiased empirical estimator. A class of test statistics based on the estimated KCMD is constructed, and a wild bootstrap test procedure to the conditional mean independence is presented. The limit distributions of the test statistics and the bootstrapped statistics under null hypothesis, fixed alternative hypothesis and local alternative hypothesis are given respectively, 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 the tests based on martingale difference divergence in monotone dependence, but excel in the cases of nonlinear relationships or the moment restriction on X is violated. Two real data examples are presented for the illustration of the proposed method.

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理学院

2023年6月14日