Log-Density Deconvolution by Wavelet Thresholding
AbstractThis paper proposes a new wavelet-based method for deconvolving a density. The estimator combines the ideas of nonlinear wavelet thresholding with periodised Meyer wavelets and estimation by information projection. It is guaranteed to be in the class of density functions, in particular it is positive everywhere by construction. The asymptotic optimality of the estimator is established in terms of rate of convergence of the Kullback-Leibler discrepancy over Besov classes. Finite sample properties is investigated in detail, and show the excellent empirical performance of the estimator, compared with other recently introduced estimators.
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Bibliographic InfoPaper provided by Toulouse School of Economics (TSE) in its series TSE Working Papers with number 09-011.
Date of creation: 11 Feb 2009
Date of revision:
deconvolution; wavelet thresholding; adaptive estimation;
Other versions of this item:
- Jérémie Bigot & Sébastien Van Bellegem, 2009. "Log-density Deconvolution by Wavelet Thresholding," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 36(4), pages 749-763.
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- Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2011.
"Convergence Rates For Ill-Posed Inverse Problems With An Unknown Operator,"
Cambridge University Press, vol. 27(03), pages 522-545, June.
- Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2011. "Convergence Rates for Ill-posed Inverse Problems with an Unknown Operator," Open Access publications from University of Toulouse 1 Capitole http://neeo.univ-tlse1.fr, University of Toulouse 1 Capitole.
- Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2009. "Convergence Rates for III-Posed Inverse Problems with an Unknown Operator," TSE Working Papers 09-030, Toulouse School of Economics (TSE).
- Johannes, Jan, 2009. "Deconvolution with unknown error distribution," Open Access publications from UniversitÃ© catholique de Louvain info:hdl:2078/127369, Université catholique de Louvain.
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