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This paper introduces a novel two-sample test for a broad class oforthogonally equivalent positive definite symmetric matrix distributions. Ourtest is the first of its kind and we derive its asymptotic distribution. Toestimate the test power, we use a warp-speed bootstrap method and consider themost common matrix distributions. We provide several real data examples,including the data for main cryptocurrencies and stock data of major UScompanies. The real data examples demonstrate the applicability of our test inthe context closely related to algorithmic trading. The popularity of matrixdistributions in many applications and the need for such a test in theliterature are reconciled by our findings.

A novel two-sample test within the space of symmetric positive definite matrix distributions and its application in finance