Work

On convergence of regularized covariance estimator based on modified Cholesky decomposition

Year: 2025

Type: article

Abstract: 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.

Source: Journal of Multivariate Analysis

DOI: 10.1016/j.jmva.2025.105553

Authors: Yuli Liang, Deliang Dai, Shaobo Jin

Institutions: Guangxi Normal University, Linnaeus University, Uppsala University

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310

Funders: Guangxi Normal University, Education Department of Guangxi Zhuang Autonomous Region