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Open AccessArticle

Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise

1
Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
2
Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow 119333, Russia
Mathematics 2020, 8(3), 377; https://doi.org/10.3390/math8030377
Received: 13 February 2020 / Revised: 2 March 2020 / Accepted: 5 March 2020 / Published: 8 March 2020
(This article belongs to the Special Issue Stability Problems for Stochastic Models: Theory and Applications)
Signal de-noising methods based on threshold processing of wavelet decomposition coefficients have become popular due to their simplicity, speed, and ability to adapt to signal functions with spatially inhomogeneous smoothness. The analysis of the errors of these methods is an important practical task, since it makes it possible to evaluate the quality of both methods and equipment used for processing. Sometimes the nature of the signal is such that its samples are recorded at random times. If the sample points form a variational series based on a sample from the uniform distribution on the data registration interval, then the use of the standard threshold processing procedure is adequate. The paper considers a model of a signal that is registered at random times and contains noise with long-term dependence. The asymptotic normality and strong consistency properties of the mean-square thresholding risk estimator are proved. The obtained results make it possible to construct asymptotic confidence intervals for threshold processing errors using only the observed data. View Full-Text
Keywords: threshold processing; random samples; long-term dependence; mean-square risk estimate threshold processing; random samples; long-term dependence; mean-square risk estimate
MDPI and ACS Style

Shestakov, O. Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise. Mathematics 2020, 8, 377.

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