Smoothing level selection for density estimators based on the moments

Abstract

AbstractThis paper introduces an approach to select the bandwidth or smoothing parameter in multiresolution (MR) density estimation and nonparametric density estimation. It is based on the evolution of the second, third and fourth central moments and the shape of the estimated densities for different bandwidths and resolution levels. The proposed method has been applied to density estimation by means of multiresolution densities as well as kernel density estimation (MRDE and KDE respectively). The results of the simulations and the empirical application demonstrate that the level of resolution resulting from the moments method performs better with multimodal densities than the Bayesian Information Criterion (BIC) for multiresolution densities estimation and the plug-in for kernel densities estimation.KEYWORDS: Multiresolution density estimationkernel density estimationbandwidthmoments and level of resolution Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 The multiresolution densities are a particular case of semiparametric models (see, [Citation12,Citation14]).2 This is a well-known fact underlying all the bandwidth selection methods.3 Remind that these intervals form a partition of the real line and their amplitude converges to zero as j increases.4 Unless this is done parametrically using the EM algorithm on a mixture model of three double exponential distributions. But for a sample of size 10,000 the process time is too long.5 Note that the values for the Gini coefficient can differ from other publications since our illustration is based on gross income instead of net income.6 The expected value of the density is zero and the central and non-central moments are equal.