Bernoulli

  • Bernoulli
  • Volume 2, Number 2 (1996), 167-181.

Asymptotically efficient estimation of analytic functions in Gaussian noise

Yuri K. Golubev, Boris Y. Levit, and Alexander B. Tsybakov

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Abstract

The problem of recovery of an unknown regression function f(x), x∈R1, from noisy data is considered. The function f(.) is assumed to belong to a class of functions analytic in a strip of the complex plane around the real axis. The performance of an estimator is measured either by its deviation at a fixed point, or by its maximal error in the L-norm over a bounded interval. It is shown that in the case of equidistant observations, with an increasing design density, asymptotically minimax estimators of the unknown regression function can be found within the class of linear estimators. Such best linear estimators are explicitly obtained.

Article information

Source
Bernoulli, Volume 2, Number 2 (1996), 167-181.

Dates
First available in Project Euclid: 31 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1193839222

Digital Object Identifier
doi:10.3150/bj/1193839222

Mathematical Reviews number (MathSciNet)
MR1410136

Zentralblatt MATH identifier
0860.62034

Keywords
analytic function asymptotically minimax estimator nonparametric regression

Citation

Golubev, Yuri K.; Levit, Boris Y.; Tsybakov, Alexander B. Asymptotically efficient estimation of analytic functions in Gaussian noise. Bernoulli 2 (1996), no. 2, 167--181. doi:10.3150/bj/1193839222. https://projecteuclid.org/euclid.bj/1193839222


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