Lower bounds and aggregation in density estimation

Details Lower bounds and aggregation in density estimation Lower bounds and aggregation in density estimation

2006-03-18

arxiv.org/abs/math/0603448v1

Mathematics

Statistics Theory

Scientific paper

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.

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