Robust estimator of the correlation matrix with sparse Kronecker structure for a high-dimensional matrix-variate

Abstract It is of interest in many applications to estimate the correlation matrix of a high dimensional matrix-variate X ∈ R p × q . Existing works usually impose strong assumptions on the distribution of X such as sub-Gaussian or strong moment conditions. These assumptions may be violated easily in practice and a robust estimator is desired. In this paper, we consider the case where the correlation matrix has a sparse Kronecker structure and propose a robust estimator based on Kendall’s τ correlation. The proposed estimator is extended further to tensor data. The theoretical properties of the estimator are established, showing that Kronecker structure actually increases the effective sample size and leads to a fast convergence rate. Finally, we apply the proposed estimator to bigraphical model, obtaining an estimator of better convergence rate than the existing results. Simulations and real data analysis confirm the competitiveness of the proposed method.