Three estimators of the Mahalanobis distance in high-dimensional data

This paper treats the problem of estimating the Mahalanobis distance for the purpose of detecting outliers in high-dimensional data. Three ridge-type estimators are proposed and risk functions for deciding an appropriate value of the ridge coefficient are developed. It is argued that one of the ridge estimator has particularly tractable properties, which is demonstrated through outlier analysis of real and simulated data.