勷勤数学•专家报告

题      目：Statistical inference for ultrahigh dimensional location parameter based on spatial median

报  告  人：程光辉   讲师  (邀请人：吴琴 )

                                    广州大学

时      间：6月25日  11：15-12：15

地     点：数学院西楼二楼会议室

报告人简介:

       程光辉, 统计学博士, 2017年12月博士毕业于东北师大数学与统计学院, 现任广州大学金融研究院讲师。主持国家青年基金一项，广东省省面上基金一项，并在 Annals of Statistics，Biometrika，Scandinavian journal of statistics , CSDA等权威统计期刊发表多篇论文。

摘      要：

Motivated by the widely used geometric median-of-means estimator in machine learning, this paper studies statistical inference for ultrahigh dimensionality location parameter based on the sample spatial median under a general multivariate model, including simultaneous confidence intervals construction, global tests, and multiple testing with false discovery rate control, as well as asymptotic relative efficiency of the sample spatial median relative to the sample mean.

To achieve these goals, we derive a novel Bahadur representation of the sample spatial median with a maximum-norm bound on the remainder term, and establish Gaussian approximation for the sample spatial median over the class of hyperrectangles. In addition, a multiplier bootstrap algorithm is proposed to approximate the distribution of the sample spatial median.

The approximations are valid when the dimension diverges at an exponentially rate of the sample size, which facilitates the application of the spatial median in the ultrahigh dimensional region. Moreover, we extend the Gaussian and bootstrap approximations to the two-sample problem, when the difference between two location parameter is of interest. The proposed approaches are further illustrated by simulations and analysis of a genomic dataset from a microarray study。

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