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Biometrika 1985 72(1):109-116; doi:10.1093/biomet/72.1.109
© 1985 by Biometrika Trust
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Interval estimation in discrimination: The multivariate normal equal covariance case

FRANK CRITCHLEY and IAN FORD

Department of Statistics, University of Warwick Coventry CV4 7AL, U.K
Department of Statistics, University of Glasgow Glasgow G12 8QW, U.K

A general approach to discrimination problems is described which emphasizes the viewpoint of individual cases and expresses the uncertainty with which individual decisions are made. It is applied to the particular case of two multivariate normal distributions with a common covariance matrix. An affine transformation, to which the key quantities are invariant, simplifies discussion of the distribution of the estimated log odds ratio and suggests a practically useful plot which generalizes the usual display of discriminant scores and has several attractive features. An illustration is given. Two approximate interval estimation techniques for the true log odds ratio are described and evaluated in a range of practical situations by a simulation study. Some further applications of our general approach are briefly indicated.

Key Words: Discrimination • Graphical display • Interval estimation • Simulation study


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