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Estimation of large sparse covariance matrices is of great importance forstatistical analysis, especially in the high-dimensional settings. Thetraditional approach such as the sample covariance matrix performs poorly dueto the high dimensionality. The modified Cholesky decomposition (MCD) is acommonly used method for sparse covariance matrix estimation. However, the MCDmethod relies on the order of variables, which is often not available or cannotbe pre-determined in practice. In this work, we solve this order issue byobtaining a set of covariance matrix estimates under different orders ofvariables used in the MCD. Then we consider an ensemble estimator as the"center" of such a set of covariance matrix estimates with respect to theFrobenius norm. The proposed method not only ensures the estimator to bepositive definite, but also can capture the underlying sparse structure of thecovariance matrix. Under some weak regularity conditions, we establish bothalgorithmic convergence and asymptotical convergence of the proposed method.The merits of the proposed method are illustrated through simulation studiesand one real data example.

On Variable Ordination of Modified Cholesky Decomposition for Sparse Covariance Matrix Estimation