Risk Bounds for Density Estimation
Motivation: Li and Barron [6, 7] give a greedy method for estimating densities by a finite mixture. The trade-off between approximation and estimation error is present in their risk bound in terms of the optimal number of components used for density estimation. Using techniques from Empirical Process theory [11] and results from geometry in Banach Spaces [5], we improve the bounds and show that, in fact, the estimation bound does not depend on the number of components.