We propose a new nonparametric estimator for the density function of multivariate bounded data. As frequently observed in practice, the variables may be partially bounded (e.g., nonnegative) or completely bounded (e.g., in the unit interval). In addition, the variables may have a point mass. We...

Let (X, Y) be an d--valued regression pair, whereXhas a density andYis bounded. Ifni.i.d. samples are drawn from this distribution, the Nadaraya-Watson kernel regression estimate in dwith Hilbert kernelK(x)=1/||x||dis shown to converge weakly for all such regression pairs. We also show that...

Likelihood-based cross-validation is a statistical tool for selecting a density estimate based on n i.i.d. observations from the true density among a collection of candidate density estimators. General examples are the selection of a model indexing a maximum likelihood estimator, and the...