Simultaneous wavelet deconvolution in periodic setting
Abbreviated Journal Title
Scand. J. Stat.
deconvolution; Meyer wavelets; multichannel system; non-parametric; regression; DENSITY DECONVOLUTION; INVERSE PROBLEMS; DECOMPOSITION; REGRESSION; Statistics & Probability
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.
Scandinavian Journal of Statistics
"Simultaneous wavelet deconvolution in periodic setting" (2006). Faculty Bibliography 2000s. 6063.