Bernoulli

  • Bernoulli
  • Volume 5, Number 6 (1999), 1099-1118.

The asymptotic minimax constant for sup-norm loss in nonparametric density estimation

Alexander Korostelev and Michael Nussbaum

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Abstract

We develop the exact constant of the risk asymptotics in the uniform norm for density estimation. This constant has already been found for nonparametric regression and for signal estimation in Gaussian white noise. Hölder classes for arbitrary smoothness index β>0 on the unit interval are considered. The constant involves the value of an optimal recovery problem as in the white noise case, but in addition it depends on the maximum of densities in the function class.

Article information

Source
Bernoulli, Volume 5, Number 6 (1999), 1099-1118.

Dates
First available in Project Euclid: 23 March 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1143122304

Mathematical Reviews number (MathSciNet)
MR1735786

Zentralblatt MATH identifier
0955.62037

Keywords
density estimation exact constant optimal recovery uniform norm risk white noise

Citation

Korostelev, Alexander; Nussbaum, Michael. The asymptotic minimax constant for sup-norm loss in nonparametric density estimation. Bernoulli 5 (1999), no. 6, 1099--1118. https://projecteuclid.org/euclid.bj/1143122304


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