{\it J. Aitchison} and {\it C. G. G. Aitken} [ibid. 63, 413-420 (1976; Zbl 0344.62035)] proposed a kernel method for estimating the cell probabilities of a multivariate categorical distribution, which method involved an unknown smoothing parameter $λ$. This paper gives a method of estimating $λ$, which is connected to multivariate discrimination and based on maximization of the leaving-one-out estimator of the nonerror rate. It is shown that this estimate is Bayes risk strongly consistent.
Reviewer: Chen Guijing