題目: Mean or Median in High dimensions? A perspective from Gaussian approximation
報告人：程光輝
邀請人：段江濤
騰訊會議ID： 685-7293-1289
時間：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.
簡介：
程光輝，廣州大學(xué)副教授、碩士生導(dǎo)師, 統(tǒng)計學(xué)博士, .研究領(lǐng)域為高維隨機(jī)矩陣結(jié)構(gòu)統(tǒng)計推斷，相依數(shù)據(jù)分析；高斯逼近方法的應(yīng)用， 在Annals of Statistics，Biometrika，Biometrics, Statistica Sinica, Statistics and Computing，Scandinavian Journal of Statistics， CSDA 等權(quán)威統(tǒng)計期刊發(fā)表多篇論文。
