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Journal of Mathematical Sciences

, Volume 234, Issue 6, pp 810–815 | Cite as

The Asymptotic Behavior of the Optimal Threshold Minimizing the Probability-of-Error Criterion

  • A. A. Kudryavtsev
  • O.V. ShestakovEmail author
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In this paper we consider the problem of estimation of a signal function from the noised observations via thresholding its wavelet coefficients. We find the asymptotic order of the optimal threshold that minimizes the probability of the maximum error between the estimates and the true wavelet coefficients exceeding a critical value.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical Statistics, Faculty of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussia
  2. 2.Institute of Informatics ProblemsFederal Research Center “Computer Science and Control” of the Russian Academy of SciencesMoscowRussia

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