On convergence of regularized covariance estimator based on modified Cholesky decomposition
研究了基于修正Cholesky分解的惩罚似然方法，通过结合收缩和平滑惩罚构造协方差矩阵估计量，并在正则条件下建立了其收敛性质，填补了理论空白。
The regularization for covariance matrix is a widely used technique when estimating large covariance matrices. This paper examines a penalized likelihood method for constructing a statistically efficient covariance matrix estimator. Modified Cholesky decomposition (MCD) is used to parameterize the covariance matrix and the effective regularization scheme is achieved by combining both shrinkage and smoothing penalties on the Cholesky factor. The practical performance is at odds with an absence of theoretical properties of the derived estimators in the literature. In this work, we aim to fill the gap between theory and practice by establishing the convergence properties under regularity conditions. We also provide a simulation study as numerical illustrations.