A note on adaptive wavelet estimation in a shifted curves model via block thresholding
Résumé
In this paper, the problem of adaptive estimation of a mean pattern in a randomly shifted curve model is considered. Adopting the new point of view of Bigot and Gadat (2008), we develop an adaptive estimator based on wavelet block thresholding. Taking the minimax approach, we prove that it attains near optimal rates of convergence under the quadratic risk over a wide range of Besov balls. In comparison to the procedure of Bigot and Gadat (2008), we gain a logarithmic term in the rates of convergence (for the regular zone).
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