Cross-validation and the estimation of probability distributions with categorical data

In this paper, we consider the problem of estimating a joint distribution that is defined over a set of discrete variables. We use a smoothing kernel estimator to estimate the joint distribution. We allow for the case in which some of the discrete variables are uniformly distributed, and explicitly address the vector-valued smoothing parameter case due to its practical relevance. We show that the cross-validated smoothing parameters differ in …