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We consider the estimation of an unknown function f for weakly dependent data (α-mixing) in a general setting. Ourcontribution is theoretical: we prove that a hard thresholding wavelet estimator attains a sharp rate of convergence under the mean integratedsquared error (MISE) over Besov balls without imposing too restrictive assumptions on the model. Applications are given for two types of inverseproblems: the deconvolution density estimation and the density estimationin a GARCH-type model, both improve existing results in this dependentcontext. Another application concerns the regression model with randomdesign.

A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence