Abstract: Estimating the covariance matrix of a high-dimensional matrix-variate is an important issue. As such, many methods have been developed, typically based on the sample covariance matrix under a Gaussian or sub-Gaussian assumption. However, the sub-Gaussian assumption is restrictive and the estimate based on the sample covariance matrix is not robust. In this study, we estimate the covariance matrix of a high-dimensional matrix-variate using a transelliptical distribution and Kendall's τ correlation. Because the covariance matrix of a matrix-variate is commonly assumed to have a low-dimensional structure, we consider the structure of the Kronecker expansion. The asymptotic results of the estimator are established. Simulation results and a real-data analysis confirm the effectiveness of our method.

Key words and phrases: Kronecker product, latent covariance (correlation) matrix, matrix-variate, robust estimate.