Peter S. Karlsson

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.

Estimating mean-standard deviation ratios of financial data

This article treats the problem of linking the relation between excess return and risk of financial assets when the returns follow a factor structure. The authors propose three different estimators and their consistencies are established in cases when the number of assets in the cross-section (n) and the number of observations over time (T) are of comparable size. An empirical investigation is conducted on the Stockholm stock exchange market where the mean-standard deviation ratio is calculated for small- mid- and large cap segments, respectively.

Expected and unexpected values of individual Mahalanobis distances

ABSTRACT This paper derives first-order sampling moments of individual Mahalanobis distances (MDs) in cases when the dimension p of the variable is proportional to the sample size n. Asymptotic expected values when n, p → ∞ are derived under the assumption p/n → c, 0 ⩽ c < 1. It is shown that some types of standard estimators remain unbiased in this case, while others are asymptotically biased, a property that appears to be unnoticed in the literature. Second-order moments are also supplied to give some additional insight to the matter.