On a Novel Two-Sample Test for Matrix Distributions and Application in Finance

Abstract

The complexity of data gathered in recent years has increased the popularity of matrix methods. The primary focus of this presentation will be to discuss recent developments in testing statistical hypotheses in the field of matrix distributions. Specifically, we will explore a newly proposed test for evaluating the equality of two symmetric positive definite matrix distributions. This test is constructed by integrating the squared difference of two empirical Hankel transforms using the Wishart measure. Particular attention will be given to the application of the aforementioned test in finance, specifically in relation to major cryptocurrencies like Bitcoin and Ethereum, as well as the analysis of Bitcoin-related events Fruehwirt et al. (2021). Moreover, recent Bitcoin-related events will also be considered. Lastly, the presentation will include the application of novel tests to datasets from major S&P 500 companies Péli (2023).