报告题目：基于几何中位数和bootstrap的高维MANOVA

报告时间：2024-07-01   15:00-16:30

报  告 人：彭柳华  副教授（墨尔本大学）

报告地点：理学院东北楼二楼报告厅（209）

Abstract: The geometric median, which is applicable to high-dimensional data, can be viewed as a generalization of the univariate median used in one dimensional data. It can be used as a robust estimator for identifying the location of multi-dimensional data and has a wide range of applications in real-world scenarios. This paper explores the problem of high-dimensional multivariate analysis of variance (MANOVA) using the geometric median. A maximum-type statistic is introduced that relies on the differences between the geometric medians among various groups. The distribution of the new testing statistic is derived under the null hypothesis using Gaussian approximations, and its consistency under the alternative hypothesis is demonstrated. To approximate the distribution of the new statistic in high dimensions, a wild bootstrap algorithm is proposed and theoretically justified. Through simulation studies conducted across a variety of dimensions and sample sizes, we demonstrate the finite-sample performance of our MANOVA method based on the geometric median. We implement the proposed approach to analyze a breast cancer gene expression dataset.