Bernoulli

  • Bernoulli
  • Volume 10, Number 2 (2004), 187-220.

On minimax density estimation on \mathbb{R}}

Anatoli Juditsky and Sophie Lambert-Lacroix

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Abstract

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.

Article information

Source
Bernoulli, Volume 10, Number 2 (2004), 187-220.

Dates
First available in Project Euclid: 19 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1082380217

Digital Object Identifier
doi:10.3150/bj/1082380217

Mathematical Reviews number (MathSciNet)
MR2046772

Zentralblatt MATH identifier
1076.62037

Keywords
adaptive estimation minimax estimation nonparametric density estimation

Citation

Juditsky, Anatoli; Lambert-Lacroix, Sophie. On minimax density estimation on \mathbb{R}}. Bernoulli 10 (2004), no. 2, 187--220. doi:10.3150/bj/1082380217. https://projecteuclid.org/euclid.bj/1082380217


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