Density estimation using non-parametric and semi-parametric mixtures

摘要

This article presents a general framework for univariate non-parametric density estimation, based on mixture models. Similar to kernel-based estimation, the proposed approach uses bandwidth to control the density smoothness, but each density estimate for a fixed bandwidth is determined by non-parametric likelihood maximization, with bandwidth selection carried out as model selection. This leads to simple models, yet with higher accuracy, especially in terms of the Kullback-Leibler or the Hellinger risk. The particular problem of estimating a symmetric density function is investigated. Both simulation study and real-world data examples suggest that the mixture-based estimators outperform their kernel-based counterparts.