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

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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Correspondence to A. A. Eroshenko.

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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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Keywords

  • Wavelets
  • homogeneous linear operator
  • thresholding
  • unbiased risk estimate
  • correlated noise
  • asymptotic normality