Testing for the equality of matrix distributions in the space of positive semi-definite random matrices

Abstract

Due to numerous applications, matrix distributions have grown in popularity over the years. Although they capture the attention of the wide scientific community, the results in the field of model specification testing are still sparse. The purpose is to introduce a novel two-sample test for comparing two matrix distributions in the space of positive semi-definite random matrices and show its potential applications in finance. The test is derived as an integral difference of the empirical Hankel transforms with respect to a Wishart measure. The results of a wide empirical study that justifies its usage is presented for the novel statistic.