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Log-density Deconvolution by Wavelet Thresholding

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  • JÉRÉMIE BIGOT
  • SÉBASTIEN VAN BELLEGEM

Abstract

This paper proposes a new wavelet-based method for deconvolving a density. The estimator combines the ideas of non-linear wavelet thresholding with periodized 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 the rate of convergence of the Kullback-Leibler discrepancy over Besov classes. Finite sample properties are investigated in detail, and show the excellent empirical performance of the estimator, compared with other recently introduced estimators. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.

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Bibliographic Info

Article provided by Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association in its journal Scandinavian Journal of Statistics.

Volume (Year): 36 (2009)
Issue (Month): 4 ()
Pages: 749-763

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Handle: RePEc:bla:scjsta:v:36:y:2009:i:4:p:749-763

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Cited by:
  1. Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2011. "Convergence Rates For Ill-Posed Inverse Problems With An Unknown Operator," Econometric Theory, Cambridge University Press, vol. 27(03), pages 522-545, June.

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