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Lower bounds and aggregation in density estimation | | Guillaume Lecué
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18 Mar 2006 | | Subject: | Statistics | | 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. | | Source: | arXiv, math/0603448 | | Services: | Forum | Review | PDF | Favorites | |
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