Abstract
We consider the model: Y = X + ε, where X and ε are independent random variables. The density of ε is known whereas the one of X is a finite mixture with unknown components. Considering the “ordinary smooth case” on the density of ε, we want to estimate a component of this mixture. To reach this goal, we develop two wavelet estimators: a nonadaptive based on a projection and an adaptive based on a hard thresholding rule. We evaluate their performances by considering the mean integrated squared error over Besov balls. We prove that the adaptive one attains a sharp rate of convergence.
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Chesneau, C. Wavelet density estimators for the deconvolution of a component from a mixture. Sankhya A 73, 245–266 (2011). https://doi.org/10.1007/s13171-011-0017-x
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DOI: https://doi.org/10.1007/s13171-011-0017-x