Existence of penalised likelihood estimates and posterior propriety of separable prior distributions for Gaussian precision matrices
高斯精度矩阵的惩罚似然估计存在性与可分离先验的后验适定性
Penalised likelihoods are often used for sparse estimation of a Gaussian precision matrix. In high dimensional settings where the matrix dimension is larger than the sample size, the sample covariance matrix $S$ is not of full rank and the maximum likelihood estimate of the precision matrix does not exist. An additional advantage of some penalised likelihood estimates, for example the graphical lasso, is that it can exist even in such high dimensional settings. This paper…