Tests for large-dimensional shape matrices via Tyler's M estimators.

ABSTRACT: Tyler's M estimator, as a robust alternative to the sample covariance matrix, has been widely applied in robust statistics. However, classical theory on Tyler's M estimator is mainly developed in the low-dimensional regime for elliptical populations. It remains largely unknown when the parameter of dimension p grows proportionally to the sample size n for general populations. By utilizing the eigenvalues of Tyler's M estimator, this article develops tests for the identity and equality of shape matrices in a large-dimensional framework where the dimension-to-sample size ratio p/n has a limit in (0,1). The proposed tests can be applied to a broad class of multivariate distributions including the family of elliptical distributions (see model (2.1) below for details). To analyze both the null

SUBMITTER: Li R 

PROVIDER: S-EPMC12140177 | biostudies-literature | 2025

REPOSITORIES: biostudies-literature