Abstract Some linkages between kernel and penalty methods of density estimation are explored. It is recalled that classical Gaussian kernel density estimation can be viewed as the solution of the heat equation with initial condition given by data. We then observe that there is a direct...

Estimation of mixture densities for the classical Gaussian compound decision problem and their associated (empirical) Bayes rules is considered from two new perspectives. The first, motivated by Brown and Greenshtein, introduces a nonparametric maximum likelihood estimator of the mixture density...