Tests for proportionality of matrices with large dimension

A test for proportionality of two covariance matrices with large dimension, possibly larger than the sample size, is proposed. The statistic simple, computationally efficient, and can be used a class multivariate distributions including normality. properties statistic, asymptotic distribution, are given under high-dimensional set up. Through simulations, shown to perform accurately, outperform its recent competitors, constructed on basis similar principles. An extension multi-sample case given.