Kernel Estimators for Cell Probabilities

B. Grund

Journal of Multivariate Analysis, 1993, vol. 46, issue 2, 283-308

Abstract: Kernel density estimators for discrete multivariate data are investigated, using the notation framework of contingency tables. We derive large sample properties of kernel estimators and the least-squares cross-validation method for choosing the bandwidth, including the asymptotic bias, the mean summed squared error, the actual summed squared error, and the asymptotic distribution of the resulting non-parametric estimator. We show that the least-squares cross-validation procedure is superior to Kullback-Leibler cross-validation in terms of mean summed squared error, but that the least-squares cross-validation is still sub-optimal concerning actual summed squared error.

Date: 1993
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