Systems and Means of Informatics
2019, Volume 29, Issue 2, pp 3138
CONVERGENCE OF THE DISTRIBUTION OF THE THRESHOLD PROCESSING RISK ESTIMATE TO A MIXTURE OF NORMAL LAWS AT A RANDOM SAMPLE SIZE
Abstract
The popularity of signal processing algorithms using wavelet analysis methods has increased significantly over the past decades. This is explained by the fact that the wavelet decomposition is a convenient mathematical apparatus capable of solving problems in which the use of traditional Fourier analysis is ineffective. The main tasks for which the methods of wavelet analysis are used are signal compression and noise removal. In this case, the most commonly used method is threshold processing of wavelet expansion coefficients, which zeroes coefficients not exceeding a given threshold. The presence of noise and threshold processing procedures inevitably lead to errors in the estimated signal.
The properties of estimates of such errors (mean square risk) have been studied in many papers. In particular, it has been shown that under certain conditions, the risk estimate is strongly consistent and asymptotically normal. When using threshold processing methods, it is usually assumed that the number of wavelet coefficients is fixed. However, in some situations, the sample size is not known in advance and is modeled by a random variable. In this paper, a model with a random number of observations is considered and a class of distributions is described that can be limiting for the meansquare risk estimate.
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[+] About this article
Title
CONVERGENCE OF THE DISTRIBUTION OF THE THRESHOLD PROCESSING RISK ESTIMATE TO A MIXTURE OF NORMAL LAWS AT A RANDOM SAMPLE SIZE
Journal
Systems and Means of Informatics
Volume 29, Issue 2, pp 3138
Cover Date
20190530
DOI
10.14357/08696527190203
Print ISSN
08696527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
threshold processing; random sample size; mean square risk estimate
Authors
O. V. Shestakov ,
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 152 Leninskiye Gory, GSP1, Moscow 119991, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 442 Vavilov Str., Moscow 119333, Russian Federation
