Informatics and Applications
2019, Volume 13, Issue 2, pp 16-21
PROPERTIES OF WAVELET ESTIMATES OF SIGNALS RECORDED AT RANDOM TIME POINTS
Abstract
Wavelet analysis algorithms in combination with threshold processing procedures are widely used in nonparametric regression problems when estimating the signal function from noisy data. The advantages of these methods are their computational efficiency and the ability to adapt to the local features of the function being estimated. The error analysis of threshold processing methods is an important practical task, since it allows assessing the quality ofboth the methods themselves and the equipment used. Sometimes, the nature ofthe data is such that observations are recorded at random times. Ifthe sampling points form a variation series constructed from a sample of a uniform distribution over the data recording interval, then the use of conventional threshold processing procedures is adequate. In this paper, the author analyzes the estimate of the mean square risk of threshold processing and shows that under certain conditions, this estimate is strongly consistent and asymptotically normal.
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[+] About this article
Title
PROPERTIES OF WAVELET ESTIMATES OF SIGNALS RECORDED AT RANDOM TIME POINTS
Journal
Informatics and Applications
2019, Volume 13, Issue 2, pp 16-21
Cover Date
2019-06-30
DOI
10.14357/19922264190203
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelets; threshold processing; random samples; mean square risk estimate
Authors
O.V. Shestakov1  , 
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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