Limiting spectral distribution for a class of random matrices
Journal of Multivariate Analysis
On the empirical distribution of eigenvalues of a class of large dimensional random matrices
Journal of Multivariate Analysis
Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices
Journal of Multivariate Analysis
On limit theorem for the eigenvalues of product of two random matrices
Journal of Multivariate Analysis
First-Order Methods for Sparse Covariance Selection
SIAM Journal on Matrix Analysis and Applications
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The existence of a limiting spectral distribution (LSD) for a large-dimensional sample covariance matrix generated by the vector autoregressive moving average (VARMA) model is established. In particular, we obtain explicit forms of the LSDs for random matrices generated by a first-order vector autoregressive (VAR(1)) model and a first-order vector moving average (VMA(1)) model, as well as random coefficients for VAR(1) and VMA(1). The parameters for these explicit forms are also estimated. Finally, simulations demonstrate that the results are effective.