Combining local and global smoothing in multivariate density estimation

Nonparametric estimation of a multivariate density estimation is tackled via a method which combines traditional local smoothing with a form of global smoothing but without imposing a rigid structure. Simulation work delivers encouraging indications on the effectiveness of the method. An application to density-based clustering illustrates a possible usage. Consider estimation of the probability density function f(·) of a continuous random variable in cases when a parametric formulation for f is not considered appropriate. Given a random sample drawn form f, a variety of nonparametric estimation methods are available.