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

翻译：本文针对一类广泛的正交等价正定对称矩阵分布，提出了一种新颖的双样本检验。我们的检验是同类中的首个，并推导了其渐近分布。为估计检验功效，我们采用了加速自举方法，并考虑了最常见的矩阵分布。我们提供了多个实际数据案例，包括主要加密货币数据和美国大型公司的股票数据。这些实际数据案例证明了我们的检验在与算法交易紧密相关的背景下的适用性。矩阵分布在众多应用中的普及以及文献中对这类检验的需求，通过我们的发现得到了调和。