A novel goodness-of-fit test for the Wishart distribution based on a Stein-type characterization
Conference
65th ISI World Statistics Congress 2025
Format: IPS Abstract - WSC 2025
Keywords: characterization, goodness-of-fit,, random matrix theory
Session: IPS 836 - Stein's Method and Statistics
Thursday 9 October 2 p.m. - 3:40 p.m. (Europe/Amsterdam)
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.