Abstract
SUMMARY 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. Some key works: 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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