A Laplace transform-based test for the equality of positive semidefinite matrix distributions

TL;DR

This paper introduces a new statistical test based on Laplace transforms to compare matrix distributions, demonstrating its effectiveness through power studies and real-world financial data applications.

Contribution

It proposes a novel Laplace transform-based method for testing equality of positive semidefinite matrix distributions, with extensive performance evaluation.

Findings

The test accurately detects distribution differences in simulations.

It performs well on financial and insurance datasets.

Optimal parameters enhance test power.

Abstract

In this paper, we present a novel test for determining equality in distribution of matrix distributions. Our approach is based on the integral squared difference of the empirical Laplace transforms with respect to the noncentral Wishart measure. We conduct an extensive power study to assess the performance of the test and determine the optimal choice of parameters. Furthermore, we demonstrate the applicability of the test on financial and non-life insurance data, illustrating its effectiveness in practical scenarios.