Regularized estimation of the Mahalanobis distance based on modified Cholesky decomposition

Abstract

Estimating inverse covariance matrix is an essential part of many statistical methods. This paper proposes a regularized estimator for the inverse covariance matrix. Modified Cholesky decomposition (MCD) is utilized to construct positive definite estimators. Instead of directly regularizing the inverse covariance matrix itself, we impose regularization on the Cholesky factor. The estimated inverse covariance matrix is used to build Mahalanobis distance (MD). The proposed method is evaluated by detecting outliers through simulations and empirical studies.