A novel goodness-of-fit test for the Wishart distribution based on a Stein-type characterization

Abstract

The Wishart distribution is one of the most prominent distributions for symmetric positive definite random matrices, with numerous applications in different fields. However, the literature lacks a comprehensive set of goodness-of-fit tests specifically designed for matrix distributions. In this work, we address this gap by introducing a novel class of goodness-of-fit tests for the Wishart distribution, based on integral transforms and Stein-type identities. The proposed tests will be presented in detail, and their effectiveness will be demonstrated through an extensive empirical study, showcasing their competitiveness against existing methods.