High-Dimensional Multivariate Analysis of Variance via Geometric Median and Bootstrapping

Authors

Guanghui Cheng
Ruitao Lin
Liuhua Peng

Language

English

Publication Date

7-1-2024

Journal

Biometrics

DOI

10.1093/biomtc/ujae088

PMID

39248122

PMCID

PMC11381952

PubMedCentral® Posted Date

9-9-2024

PubMedCentral® Full Text Version

Post-print

Abstract

The geometric median, which is applicable to high-dimensional data, can be viewed as a generalization of the univariate median used in 1-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 that relies on the differences between the geometric medians among various groups is introduced. The distribution of the new test statistic is derived under the null hypothesis using Gaussian approximations, and its consistency under the alternative hypothesis is established. 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, sample sizes, and data-generating models, we demonstrate the finite-sample performance of our geometric median-based MANOVA method. Additionally, we implement the proposed approach to analyze a breast cancer gene expression dataset.

Keywords

Humans, Multivariate Analysis, Breast Neoplasms, Computer Simulation, Algorithms, Models, Statistical, Female, Data Interpretation, Statistical, Gene Expression Profiling, Sample Size, Biometry, bootstrap approximation, geometric median, high-dimensional data, MANOVA

Published Open-Access

yes

Recommended Citation

Guanghui Cheng, Ruitao Lin, and Liuhua Peng, "High-Dimensional Multivariate Analysis of Variance via Geometric Median and Bootstrapping" (2024). Faculty, Staff and Student Publications. 6162.
https://digitalcommons.library.tmc.edu/uthgsbs_docs/6162