Confidence intervals for the mahalanobis distance

Benjamin Reiser

doi:10.1081/SAC-100001856

Confidence intervals for the mahalanobis distance

Benjamin Reiser

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	37-45
Number of pages	9
Journal	Communications in Statistics Part B: Simulation and Computation
Volume	30
Issue number	1
DOIs	https://doi.org/10.1081/SAC-100001856
State	Published - 2001

Keywords

Generalized Roc criterion
Noncentral F
Optimal error rate
Overlapping coefficient

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation

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10.1081/SAC-100001856

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AB - 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.

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KW - Noncentral F

KW - Optimal error rate

KW - Overlapping coefficient

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JO - Communications in Statistics Part B: Simulation and Computation

JF - Communications in Statistics Part B: Simulation and Computation

IS - 1

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Confidence intervals for the mahalanobis distance

Abstract

Keywords

ASJC Scopus subject areas

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