Multivariate density estimation: A comparative study

Abstract

This paper is a continuation of the authors' earlier work [1], where a version of the Tråvén's [2] Gaussian clustering neural network (being a recursive counterpart of the EM algorithm) has been investigated. A comparative simulation study of the Gaussian clustering algorithm [1], two versions of plug-in kernel estimators and a version of Friedman's projection pursuit algorithm are presented for two- and three-dimensional data. Simulations show that the projection pursuit algorithm is a good or a very good estimator, provided, however, that the number of projections is suitably chosen. Although practically confined to estimating normal mixtures, the simulations confirm general reliability of plug-in estimators, and show the same property of the Gaussian clustering algorithm. Indeed, the simulations confirm the earlier conjecture that this last estimator proivdes a way of effectively estimating arbitrary and highly structured continuous densities on R^d, at least for small d, either by using this estimator itself or, rather, by using it as a pilot estimator for a newly proposed plug-in estimator.