Mahalanobis distance under non-normality

Tiku M. L., Islam M. Q., Qumsiyeh S. B.

STATISTICS, vol.44, no.3, pp.275-290, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 3
  • Publication Date: 2010
  • Doi Number: 10.1080/02331880903043223
  • Journal Name: STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.275-290
  • Keywords: covariance matrix, least squares, Mahalanobis distance, maximum likelihood, modified maximum likelihood, multivariate, non-normality, LINEAR-REGRESSION MODEL, CONFIDENCE-INTERVALS, MAXIMUM-LIKELIHOOD, ROBUST ESTIMATION, VARIANCE, DESIGN, DISTRIBUTIONS, PARAMETERS
  • Middle East Technical University Affiliated: Yes

Abstract

We give a novel estimator of Mahalanobis distance D2 between two non-normal populations. We show that it is enormously more efficient and robust than the traditional estimator based on least squares estimators. We give a test statistic for testing that D2=0 and study its power and robustness properties.