Asymptotically Optimal Wavelet Thresholding
in Models with Non-Gaussian Noise Distributions
A. A. Kudryavtseva* and O. V. Shestakova,b**
Translated by O. Sipacheva
a Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991 Russia
b Institute of Informatics Problems, Federal Research Center “Computer Science and Control,” Russian Academy
of Sciences, Moscow, 119933 Russia
Correspondence to: *e-mail: nubigena@mail.ru
Correspondence to: **e-mail: oshestakov@cs.msu.su
Received 2 June, 2016
Abstract—The problem of nonparametric estimation of a signal function by thresholding the coefficients of its wavelet decomposition is considered. In models with various noise distributions, asymptotically optimal thresholds and orders of the loss functions are calculated on the basis of probabilities of errors in the calculation of wavelet coefficients.
DOI: 10.1134/S1064562416060028