Empirical Choice of Histograms and Kernel Density Estimators

Abstract

Methods of choosing histogram width and the smoothing parameter of kernel density estimators by use of data are studied. They are based on estimators of risk functions corresponding to mean integrated squared error and the Kullback-Leibler information measure. Two closely related risk function estimators are given, one of Which is derived from cross-validation. In examples with simulated and real data the methods are applied to estimation of probability densities and the rate function of a time-depend- ent Poisson process.