A combined adaptive-mixtures/plug-in estimator of multivariate probability densities

A multivariate extension of the plug-in kernel (and filtered kernel) estimator is proposed and this uses asymptotically optimal bandwidth matrix (matrices) for a normal mixture approximation of a density to be estimated (the filtered kernel estimator uses different matrices for different clusters of data). The normal mixture approximation is provided by a recursive version of the EM algorithm whose initial conditions are in turn obtained via an application of the ideas of adaptive mixtures density estimation and AIC-based pruning. Simulations show that the estimator proposed, while it is in fact a rather complex multistage estimation process, provides a very reliable way of estimating arbitrary and highly structured continuous densities on R-2 and, hopefully, R-3. (C) 1997 Elsevier Science B.V.