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Biometrika 1987 74(4):829-840; doi:10.1093/biomet/74.4.829
© 1987 by Biometrika Trust
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Moments of linear discriminant functions and an asymptotic confidence interval for the log odds ratio

A. W. DAVIS

CSIRO Division of Mathematics and Statistics Glen Osmond, South Australia 5064, Australia

A general expression is obtained for the moments of a statistic which contains Anderson's linear discriminant function and the minimum variance unbiased estimator of the log odds ratio as special cases. The result is given in terms of certain invariant polynomials of matrix argument, and is used to derive the first four exact central moments, together with asymptotic expansions of the cumulants. This provides an alternative approach to Okamoto's expansion as an Edgeworth series. An asymptotic confidence interval is also obtained for the log odds ratio, using a method of Peers & Iqbal (1985), which allows for the estimation of nuisance parameters. Simulation shows that the interval has quite good properties over a range of parameter values.

Key Words: Asymptotic confidence interval • Cumulant • Discriminant analysis • Invariant polynomial • Linear discriminant function • Log odds ratio • Nuisance parameter • Simulation study • SU curve • Zonal polynomial


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