Risk Bounds for Mixture Density Estimation
Alexander Rakhlin, Dmitry Panchenko, Sayan Mukherjee · 2004
In this paper we focus on the problem of estimating a bounded density using a finite combination of densities from a given class.We consider the Maximum Likelihood Procedure (MLE) and the greedy procedure described by Li and Barron [6,7].Approximation and estimation bounds are given for the above methods.We extend and improve upon the estimation results of Li and Barron, and in particular prove an O( 1√ n ) bound on the estimation error which does not depend on the number of densities in the estimated combination.