On nonparametric multivariate binary discrimination

Aitchison & Aitken (1976) introduced a novel and ingenious nonparametric method for estimating probabilities in a multidimensional binary space. The technique is designed for use in multivariate binary discrimination. Their estimator depends crucially on an unknown smoothing parameter A, and Aitchison & Aitken proposed a maximum likelihood method for determining A from the sample. Unfortunately this leads to an adaptive estimator which can behave very erratically when there are a number of empty or near empty cells present. We demonstrate this both theoretically and by example. To overcome these difficulties we introduce another method of estimating A which is designed to minimize a global function of the mean squared error.