A. A. Kudriavtsev, O. V. Shestakov, “Estimation of the optimal rate of the wavelet thresholding risk based on the error probabilities”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2016, Issue 1,Pages <nobr>5

Theory of Probability and Mathematical Statistics

Estimation of the optimal rate of the wavelet thresholding risk based on the error probabilities

A. A. Kudriavtsev^a, O. V. Shestakov^ab

^a Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
^b Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences

Abstract: We consider the method of estimating the signal function from the noised observations based on the minimization of the probabilities of errors in calculating the wavelet coefficients. In the model with additive Gaussian noise we find the optimal parameters and estimate the risk rate.

Keywords: wavelets, thresholding, risk.

UDC: 519.22

Received: 15.02.2016
Revised: 20.02.2016