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October 1999 On pointwise adaptive nonparametric deconvolution
Alexander Goldenshluger
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Bernoulli 5(5): 907-925 (October 1999).

Abstract

We consider estimating an unknown function f from indirect white noise observations with particular emphasis on the problem of nonparametric deconvolution. Nonparametric estimators that can adapt to unknown smoothness of f are developed. The adaptive estimators are specified under two sets of assumptions on the kernel of the convolution transform. In particular, kernels having the Fourier transform with polynomially and exponentially decaying tails are considered. It is shown that the proposed estimates possess, in a sense, the best possible abilities for pointwise adaptation.

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Alexander Goldenshluger. "On pointwise adaptive nonparametric deconvolution." Bernoulli 5 (5) 907 - 925, October 1999.

Information

Published: October 1999
First available in Project Euclid: 12 February 2007

zbMATH: 0953.62033
MathSciNet: MR1715444

Keywords: adaptive estimation , Deconvolution , rates of convergence

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability

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Vol.5 • No. 5 • October 1999
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