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April 2004 On minimax density estimation on \mathbb{R}}
Anatoli Juditsky, Sophie Lambert-Lacroix
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Bernoulli 10(2): 187-220 (April 2004). DOI: 10.3150/bj/1082380217


The problem of density estimation on \mathbb{R}} on the basis of an independent sample X1,..., XN with common density f is discussed. The behaviour of the minimax Lp risk, 1≤p≤∞, is studied when f belongs to a Hölder class of regularity s on the real line. The lower bound for the minimax risk is given. We show that the linear estimator is not efficient in this setting and construct a wavelet adaptive estimator which attains (up to a logarithmic factor in N) the lower bounds involved. We show that the minimax risk depends on the parameter p when p<2+ 1/s.


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Anatoli Juditsky. Sophie Lambert-Lacroix. "On minimax density estimation on \mathbb{R}}." Bernoulli 10 (2) 187 - 220, April 2004.


Published: April 2004
First available in Project Euclid: 19 April 2004

zbMATH: 1076.62037
MathSciNet: MR2046772
Digital Object Identifier: 10.3150/bj/1082380217

Rights: Copyright © 2004 Bernoulli Society for Mathematical Statistics and Probability


Vol.10 • No. 2 • April 2004
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