Current Development in Theory and Applications of Wavelets
Volume 4, Issue 2, Pages 131 - 151
(August 2010)
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WAVELET ESTIMATION OF THE DERIVATIVES OF AN UNKNOWN FUNCTION FROM A CONVOLUTION MODEL
Christophe Chesneau
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Abstract:
We observe a stochastic process where a convolution product of an unknown function f and a known function g is corrupted by Gaussian noise. We wish to estimate the dth derivatives of f from the observations. To reach this goal, we develop an adaptive estimator based on wavelet block thresholding. We prove that it achieves near optimal rates of convergence under the mean integrated squared error (MISE) over a wide range of smoothness classes. |
| Keywords and phrases: deconvolution, derivatives function estimation, wavelets, block thresholding. |
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