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February 2000 Mixing strategies for density estimation
Yuhong Yang
Ann. Statist. 28(1): 75-87 (February 2000). DOI: 10.1214/aos/1016120365


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.


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Yuhong Yang. "Mixing strategies for density estimation." Ann. Statist. 28 (1) 75 - 87, February 2000.


Published: February 2000
First available in Project Euclid: 14 March 2002

zbMATH: 1106.62322
MathSciNet: MR1762904
Digital Object Identifier: 10.1214/aos/1016120365

Primary: 62G07
Secondary: 62B10 , 62C20 , 94A29

Keywords: adaptation with respect to estimation strategies , Density estimation , minimax adaptation , rates of convergence

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 1 • February 2000
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