Smoothing level selection for density estimators based on the moments

This 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.

本文提出了一种用于多分辨率（multiresolution, MR）密度估计与非参数密度估计的带宽或平滑参数选取方法。该方法基于不同带宽与分辨率水平下的二阶、三阶、四阶中心矩的演化规律，以及对应估计密度的形态特征。本文所提方法已被应用于多分辨率密度估计与核密度估计（分别记为MRDE与KDE）两类密度估计任务中。仿真实验与实际应用结果均表明，针对多模态密度数据，矩法所得到的分辨率水平，在多分辨率密度估计任务中的表现优于贝叶斯信息准则（Bayesian Information Criterion, BIC），在核密度估计任务中的表现优于插入式带宽选择方法。