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Biometrika 1981 68(1):287-294; doi:10.1093/biomet/68.1.287
© 1981 by Biometrika Trust
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On nonparametric multivariate binary discrimination

PETER HALL

Department of Statistics, Australian National University Canberra

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 {lambda}, and Aitchison & Aitken proposed a maximum likelihood method for determining {lambda} 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 {lambda} which is designed to minimize a global function of the mean squared error.

Key Words: Binary data • Kernel estimator • Multivariate binary discrimination • Nonparametric • Robustness


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