Regularized estimation of Kronecker structured covariance matrix using modified Cholesky decomposition
Deliang Dai, Chengcheng Hao, Shaobo Jin, Yuli Liang · Journal of Statistical Computation and Simulation · 2023
In this paper, we study a Kronecker structured model for covariance matrices when data are matrix-valued.Using the modified Cholesky decomposition for Kronecker structured covariance matrix, we propose a regularized covariance estimator by imposing shrinkage and smoothing penalties on the Cholesky factors.A regularized flip-flop (RFF) algorithm is developed to produce a statistically efficient estimator for a large covariance matrix of matrix-valued data.Asymptotic properties are investigated and the performance of the estimator is evaluated by simulations.The results presented are applied to real data example.