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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Proceedings of the XXXIII International Seminar on Stability Problems for Stochastic Models, Svetlogorsk, Russia, June 12–18, 2016
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Kudryavtsev, A.A., Shestakov, O. The Asymptotic Behavior of the Optimal Threshold Minimizing the Probability-of-Error Criterion. J Math Sci 234, 810–815 (2018). https://doi.org/10.1007/s10958-018-4048-x
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DOI: https://doi.org/10.1007/s10958-018-4048-x