Title

Simultaneous Wavelet Deconvolution In Periodic Setting

Keywords

Deconvolution; Meyer wavelets; Multichannel system; Non-parametric regression

Abstract

The paper proposes a method of deconvolution in a periodic setting which combines two important ideas, the fast wavelet and Fourier transform-based estimation procedure of Johnstone et al. [J. Roy. Statist. Soc. Ser. B66 (2004) 547] and the multichannel system technique proposed by Casey and Walnut [SIAM Rev. 36 (1994) 537]. An unknown function is estimated by a wavelet series where the empirical wavelet coefficients are filtered in an adapting non-linear fashion. It is shown theoretically that the estimator achieves optimal convergence rate in a wide range of Besov spaces. The procedure allows to reduce the ill-posedness of the problem especially in the case of non-smooth blurring functions such as boxcar functions: it is proved that additions of extra channels improve convergence rate of the estimator. Theoretical study is supplemented by an extensive set of small-sample simulation experiments demonstrating high-quality performance of the proposed method. © Board of the Foundation of the Scandinavian Journal of Statistics 2006.

Publication Date

6-1-2006

Publication Title

Scandinavian Journal of Statistics

Volume

33

Issue

2

Number of Pages

293-306

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1111/j.1467-9469.2006.00463.x

Socpus ID

33745301978 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33745301978

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