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Asymptotic normality of estimating risk upon the wavelet-vaguelette decomposition of a signal function in a model with correlated noise

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Abstract

The problem of estimating the function when using a homogeneous linear operator in a model with correlated noise is considered. The asymptotic properties of estimating risk upon the threshold wavelet-vaguelette decomposition of a signal are studied. The conditions under which the asymptotic normality of an unbiased risk estimate holds are given.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    A. A. Eroshenko & O. V. Shestakov

  2. Institute of Informatics Problems, Russian Academy of Sciences, Moscow, 117333, Russia

    O. V. Shestakov

Authors
  1. A. A. Eroshenko
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  2. O. V. Shestakov
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Correspondence to A. A. Eroshenko.

Additional information

Original Russian Text © A.A. Eroshenko, O.V. Shestakov, 2014, published in Vestnik Moskovskogo Universiteta. Vychislitel’naya Matematika i Kibernetika, 2014, No. 3, pp. 23–30.

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Eroshenko, A.A., Shestakov, O.V. Asymptotic normality of estimating risk upon the wavelet-vaguelette decomposition of a signal function in a model with correlated noise. MoscowUniv.Comput.Math.Cybern. 38, 110–117 (2014). https://doi.org/10.3103/S0278641914030042

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  • DOI: https://doi.org/10.3103/S0278641914030042

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