Lower Bounds and Aggregation in Density Estimation

In this paper we prove the optimality of an aggregation procedure. We prove lower bounds for aggregation of model selection type of M density estimators for the Kullback-Leibler divergence (KL), the Hellinger's distance and the L1-distance. The lower bound, with respect to the KL distance, can be achieved by the on-line type estimate suggested, among others, by Yang (2000a). Combining these results, we state that logM/n is an optimal rate of aggregation in the sense of Tsybakov (2003), where n is the sample size.

• Type: Journal
• Year: 2006
• Where: JMLR
• Authors: Guillaume Lecué
• Keywords: Aggregation Procedure, JMLR 2006, Lower Bound, Model Selection Type