General results on adaptive density estimation are obtained with
respect to any countable collection of estimation strategies under
Kullback-Leibler and squared $L_2$ losses. It is shown that without knowing
which strategy works best for the underlying density, a single strategy can be
constructed by mixing the proposed ones to be adaptive in terms of statistical
risks. A consequence is that under some mild conditions, an asymptotically
minimax-rate adaptive estimator exists for a given countable collection of
density classes; that is, a single estimator can be constructed to be
simultaneously minimax-rate optimal for all the function classes being
considered. A demonstration is given for high-dimensional density estimation on
$[0,1]^d$ where the constructed estimator adapts to smoothness and
interaction-order over some piecewise Besov classes and is consistent for all
the densities with finite entropy.
Publié le : 2000-02-14
Classification:
Density estimation,
rates of convergence,
adaptation with respect to estimation strategies,
minimax adaptation,
62G07,
62B10,
62C20,
94A29
@article{1016120365,
author = {Yang, Yuhong},
title = {Mixing strategies for density estimation},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 75-87},
language = {en},
url = {http://dml.mathdoc.fr/item/1016120365}
}
Yang, Yuhong. Mixing strategies for density estimation. Ann. Statist., Tome 28 (2000) no. 3, pp. 75-87. http://gdmltest.u-ga.fr/item/1016120365/