We propose a new asymptotic test for the separability of a covariance matrix. The null distribution is valid in wide matrix elliptical model that includes, in particular, both matrix Gaussian and matrix $t$-distribution. The test is fast to compute and makes no assumptions about the component covariance matrices. An alternative, Wald-type version of the test is also proposed. Our simulations reveal that both versions of the test have good power even for heavier-tailed distributions and can compete with the Gaussian likelihood ratio test in the case of normal data.

翻译：本文提出了一种新的协方差矩阵可分离性渐近检验方法。该检验在原假设下的分布在广泛的矩阵椭圆模型中均成立，特别包含矩阵高斯分布与矩阵$t$分布。该检验计算速度快，且无需对分量协方差矩阵作任何假设。本文还提出了该检验的另一种沃尔德型版本。模拟研究表明，两种检验版本即使在重尾分布下仍具有良好的检验功效，并且在正态数据情形下可与高斯似然比检验相媲美。