NONPARAMETRIC MULTIVARIATE DENSITY-ESTIMATION - A COMPARATIVE-STUDY

This paper algorithmically and empirically studies two major types of nonparametric multivariate density estimation techniques, where no ass umption is made about the data being drawn from any of known parametri c families of distribution. The first type is the popular kernel metho d (and several of its variants) which uses locally tuned radial basis (e.g., Gaussian) functions to interpolate the multidimensional density ; the second type is based on an exploratory projection pursuit techni que which interprets the multidimensional density through the construc tion of several 1-D densities along highly ''interesting'' projections of multidimensional data. Performance evaluations using training data from mixture Gaussian and mixture Cauchy densities are presented. The results show that the curse of dimensionality and the sensitivity of control parameters have a much more adverse impact on the kernel densi ty estimators than on the projection pursuit density estimators.