Current Development in Theory and Applications of Wavelets
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Abstract: We consider a regression model with
errors-in-variables: where and Our aim is to estimate the unknown
regression function f and its
derivatives under mild assumptions on x (only finite moments of order 2 are required). To
reach this goal, we develop a new adaptive wavelet estimator based on a hard
thresholding rule. Taking the minimax approach under the mean integrated squared
error over Besov balls, we prove that it attains a sharp rate of convergence.
Keywords and phrases: errors-in-variables model, derivatives function estimation, minimax approach, wavelets, hard thresholding.
