Simultaneous wavelet deconvolution in periodic setting

    Authors

    D. De Canditiis;M. Pensky

    Comments

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    Abbreviated Journal Title

    Scand. J. Stat.

    Keywords

    deconvolution; Meyer wavelets; multichannel system; non-parametric; regression; DENSITY DECONVOLUTION; INVERSE PROBLEMS; DECOMPOSITION; REGRESSION; Statistics & Probability

    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.

    Journal Title

    Scandinavian Journal of Statistics

    Volume

    33

    Issue/Number

    2

    Publication Date

    1-1-2006

    Document Type

    Article

    Language

    English

    First Page

    293

    Last Page

    306

    WOS Identifier

    WOS:000237184600010

    ISSN

    0303-6898

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