- Volume 5, Number 5 (1999), 907-925.
On pointwise adaptive nonparametric deconvolution
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.
Bernoulli, Volume 5, Number 5 (1999), 907-925.
First available in Project Euclid: 12 February 2007
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Goldenshluger, Alexander. On pointwise adaptive nonparametric deconvolution. Bernoulli 5 (1999), no. 5, 907--925. https://projecteuclid.org/euclid.bj/1171290404