Nonparametric Density Estimation using Wavelets

Here the problem of density estimation using wavelets is considered. Nonparametric wavelet density estimators have recently been proposed and seem to outperform classical estimators in representing discontinuities and local oscillations. The purpose of this paper is to give a review of different types of wavelet density estimators proposed in the literature. Properties, comparisons with classical estimators and applications are stressed. Multivariate extensions are considered. Performances of wavelet estimators are analyzed using a family of normal mixture densities and the Old Faithful Geyser dataset.