Open Access
June 1996 Asymptotically efficient estimation of analytic functions in Gaussian noise
Yuri K. Golubev, Boris Y. Levit, Alexander B. Tsybakov
Bernoulli 2(2): 167-181 (June 1996). DOI: 10.3150/bj/1193839222


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.


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Yuri K. Golubev. Boris Y. Levit. Alexander B. Tsybakov. "Asymptotically efficient estimation of analytic functions in Gaussian noise." Bernoulli 2 (2) 167 - 181, June 1996.


Published: June 1996
First available in Project Euclid: 31 October 2007

zbMATH: 0860.62034
MathSciNet: MR1410136
Digital Object Identifier: 10.3150/bj/1193839222

Keywords: Analytic function , Asymptotically minimax estimator , Nonparametric regression

Rights: Copyright © 1996 Bernoulli Society for Mathematical Statistics and Probability

Vol.2 • No. 2 • June 1996
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