A family of non-parametric density estimation algorithms

Abstract

A new methodology for density estimation is proposed. The method- ology, which builds on the one developed in [15], normalizes the data points through the composition of simple maps. The parameters of each map are determined through the maximization of a local quadratic approximation to the log-likelihood. Various candidates for the el- ementary maps of each step are proposed; criteria for choosing one includes robustness, computational simplicity and good behavior in high-dimensional settings. A good choice is that of localized radial expansions, which depend on a single parameter: all the complex- ity of arbitrary, possibly convoluted probability densities can be built through the composition of such simple maps.