Lower bounds and aggregation in density estimation

Guillaume Lecué

Lower bounds and aggregation in density estimation

统计理论 2016-08-16 v1 统计理论

作者: Guillaume Lecué

摘要

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.

关键词

density estimation bound

引用

@article{arxiv.math/0603448,
  title  = {Lower bounds and aggregation in density estimation},
  author = {Guillaume Lecué},
  journal= {arXiv preprint arXiv:math/0603448},
  year   = {2016}
}

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