光华讲坛——社会名流与企业家论坛第 5884 期

（线上讲座）

主题：High-dimensional MANOVA via Bootstrapping and its Application to Functional and Sparse Count Data

主讲人：新加坡国立大学林振华博士

主持人：统计学院林华珍教授

时间：2020年11月3日（周二）上午10:30-11:30

直播平台及会议ID：腾讯会议，828 910 382

主办单位：统计研究中心和统计学院 科研处

主讲人简介：

         Lin Zhenhua is currently a Presidential Young Professor at Department of Statistics and Applied Probability, National University of Singapore. He received Bachelor' degree from Fudan University in 2008, Master degrees from Simon Fraser University in 2011 and 2013, and Ph.D. degree from University of Toronto, 2017. He was a postdoctoral fellow at University of California, Davis from 2017 and 2019. His research interest lies in funcitonal, high-dimensional and/or non-Euclidean data analysis.

    林振华是新加坡国立大学统计与应用概率系的Presidential Young Professor。他于2008年获得复旦大学学士学位，2010和2013年获得西蒙弗雷泽大学硕士学位， 2017年获得多伦多大学博士学位。2017-2019年期间，他在加州大学戴维斯分校从事博士后工作。他的研究兴趣主要为函数型数据分析，高维数据分析和非欧氏数据分析。详情请见其个人链接：https://blog.nus.edu.sg/zhenhua/

内容提要：

 We propose a new approach to the problem of high-dimensional multivariate ANOVA via bootstrapping max statistics that involve the differences of sample mean vectors, through constructing simultaneous confidence intervals for the differences of population mean vectors. The proposed method is suited to simultaneously test the equality of several pairs of mean vectors of potentially more than two populations. By exploiting the variance decay property that is a natural feature in relevant applications, we are able to provide dimension-free and nearly-parametric convergence rates for Gaussian approximation, bootstrap approximation, and the size of the test. We demonstrate the proposed approach with ANOVA problems for functional data and sparse count data. The proposed methodology is shown to work well in simulations and several real data applications.

本文提出了一种新的方法来解决高维方差分析的问题。该方法通过样本均值向量差的bootstrap最大统计量来构造总体均值向量差的联合置信区间。并且，该方法适用于同时检验多个总体的均值向量对是否相同的问题。通过利用方差衰减这一在相关应用中自然存在的特性，我们能够为高斯逼近、bootstrap逼近和检验的size提供不受变量维数影响和近似参数的收敛速度。我们用函数数据和稀疏计数数据的方差分析问题来阐释所提方法的应用广泛性。最后，该方法在仿真和实际数据应用中取得了良好的效果。