Journal of Statistical Theory and Practice

, Volume 5, Issue 2, pp 303–326 | Cite as

Adaptive Wavelet Estimator for a Function and its Derivatives in an Indirect Convolution Model

  • Christophe ChesneauEmail author


We consider an indirect convolution model where m blurred and noise-perturbed functions f1,..., fm are randomly observed. For a fixed ω ∈ {f1,..., m}, we want to estimate fω and its derivatives. An adaptive nonlinear wavelet estimator using a singular value decomposition is developed. Taking the mean integrated squared error over Besov balls, we prove that it attains a fast rate of convergence.

AMS Subject Classification

62G07 62G20 


Deconvolution Function estimation Rate of convergence Wavelets Hard thresholding 


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Copyright information

© Grace Scientific Publishing 2011

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Nicolas OresmeUniversité de Caen Basse-NormandieCaenFrance

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