题目: Mean or Median in High dimensions? A perspective from Gaussian approximation
报告人：程光辉
邀请人：段江涛
腾讯会议ID： 685-7293-1289
时间：2025年12月03日（周三） 14:00-16:00
摘要：In this talk, we 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. 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. We define asymptotic relative efficiency compared to sample mean in high dimensions. The proposed approaches are further illustrated by simulations and analysis of a genomic dataset from a microarray study.
简介：
程光辉，广州大学副教授、硕士生导师, 统计学博士, .研究领域为高维随机矩阵结构统计推断，相依数据分析；高斯逼近方法的应用， 在Annals of Statistics，Biometrika，Biometrics, Statistica Sinica, Statistics and Computing，Scandinavian Journal of Statistics， CSDA 等权威统计期刊发表多篇论文。
