Testing the proportionality of two large-dimensional covariance matrices is studied. Based on modern random matrix theory, a pseudo-likelihood ratio statistic is proposed and its asymptotic normality is proved as the dimension and sample sizes tend to infinity proportionally.

Let X1,…,Xn1+1∼iidNp(μ1,Σ1) and Y1,…,Yn2+1∼iidNp(μ2,Σ2) be two independent random samples, where pn2. In this article, we propose a new test for the proportionality of two large p×p covariance matrices Σ1 and Σ2. By applying modern random matrix theory, we establish the asymptotic...