Kernel estimators for cell probabilities

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.