Lower bounds and aggregation in density estimation

Abstract

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-Leiber divergence (KL), the Hellinger's distance and the $L\_1$-distance. The lower bound, with respect to the KL distance, can be achieved by the on-line type estimate suggested, among others, by Yang (2000). Combining these results, we state that $\log M/n$ is an optimal rate of aggregation in the sense of Tsybakov (2003), where $n$ is the sample size.

References in corpus (1)

• From $\epsilon$-entropy to KL-entropy: Analysis of minimum information complexity density estimation

Cited by in corpus (3)

• Hyper-sparse optimal aggregation
• Optimal exponential bounds for aggregation of density estimators
• Minimax Rates for Conditional Density Estimation via Empirical Entropy