A factor model based covariance matrix is used to build a new form of Mahalanobis distance. The distribution and relative properties of the new Mahalanobis distances are derived. A new type of Mahalanobis distance based on the separated part of the factor model is defined. Contamination effects...

This paper treats the problem of estimating individual Mahalanobis distances (MD) in cases when the dimension of the variable p is proportional to the sample size n. Asymptotic expected values are derived under the assumption p/n-c, 0=c1 for both the traditional and the leave-one-out estimators....

In this paper we derive central limit theorems for two different types of Mahalanobis distances in situations where the dimension of the parent variable increases proportionally with the sample size. It is shown that although the two estimators are closely related and behave similarly in nite...