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-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 log M/n is an optimal rate of aggregation in the sense of Tsybakov (2003), where n is the sample size.
Cite
Text
Lecué. "Lower Bounds and Aggregation in Density Estimation." Journal of Machine Learning Research, 2006.Markdown
[Lecué. "Lower Bounds and Aggregation in Density Estimation." Journal of Machine Learning Research, 2006.](https://mlanthology.org/jmlr/2006/lecue2006jmlr-lower/)BibTeX
@article{lecue2006jmlr-lower,
title = {{Lower Bounds and Aggregation in Density Estimation}},
author = {Lecué, Guillaume},
journal = {Journal of Machine Learning Research},
year = {2006},
pages = {971-981},
volume = {7},
url = {https://mlanthology.org/jmlr/2006/lecue2006jmlr-lower/}
}