A Family of Nonparametric Density Estimation Algorithms

Abstract A new methodology for density estimation is proposed. The methodology, which builds on the one developed by Tabak and Vanden‐Eijnden, 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 elementary 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 complexity of arbitrary, possibly convoluted probability densities can be built through the composition of such simple maps. © 2012 Wiley Periodicals, Inc.