Confidence intervals for the mahalanobis distance

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Mahalanobis distances appear, often in a disguised form, in many statistical problems dealing with comparing two multivariate normal populations. Assuming a common covariance matrix the overlapping coefficient (Bradley, E.L. Encyclopedia of Statistical Sciences; 1985), optimal error rates (Rao, P.S.R.S.; Dorvlo, A.S.S. Commun. Statist. - Simula. Computation 1985,14,774-790), and the generalized ROC criterion (Reiser, B.; Faraggi, D. Biometrics 1997,55,644-652) are all monotonie functions of the Mahalanobis distance. Approximate confidence intervals for all of these have appeared in the literature on an ad-hoc basis. In this paper, we provide a unified approach to obtaining an effectively exact confidence interval for the Mahalanobis distance and all the above measures.

Original languageEnglish
Pages (from-to)37-45
Number of pages9
JournalCommunications in Statistics Part B: Simulation and Computation
Issue number1
StatePublished - 2001


  • Generalized Roc criterion
  • Noncentral F
  • Optimal error rate
  • Overlapping coefficient

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation


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