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Biometrika 1986 73(2):405-411; doi:10.1093/biomet/73.2.405
© 1986 by Biometrika Trust
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An alternative choice of smoothing for kernel-based density estimates in discrete discriminant analysis

GERHARD TUTZ

Lehrstuhl für Statistik, Universität Regensburg D-8400 Regensburg, Federal Republic of Germany

The kernel method of estimating the cell probabilities of a multivariate categorical distribution, due to Aitchison & Aitken (1976), depends crucially on an unknown smoothing parameter {lambda}. A method of estimating A is introduced which is explicitly connected to multivariate discrimination. The method, based on maximization of the leaving-one-out estimator of the nonerror rate, is shown to be Bayes risk strongly consistent. An example is given to illustrate the application.

Key Words: Density estimation • Discrimination • Kernel method • Leaving-one-out method


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