Abstract: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 gives a thorough analysis of the existence of penalised likelihood estimates for positive semidefinite $S$. Specific tail conditions are provided on the diagonal and off-diagonal penalty functions that ensure existence of the estimate. This is also extended to the Bayesian setting where conditions on separable prior distributions are provided that ensure the resulting posterior distribution is proper.
From: Jack Storror Carter [view email]
[v1]
Mon, 26 May 2025 13:57:13 UTC (10 KB)
[v2]
Thu, 20 Aug 2026 17:45:26 UTC (25 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。