Abstract
The problem of constructing an estimate of a signal function from noisy observations, assuming that this function is uniformly Lipschitz regular, is considered. The thresholding of empirical wavelet coefficients is used to reduce the noise. As a rule, it is assumed that the noise distribution is Gaussian and the optimal parameters of thresholding are known for various classes of signal functions. In this paper a model of additive noise whose distribution belongs to a fairly wide class, is considered. The mean-square risk estimate of thresholding is analyzed. It is shown that under certain conditions, this estimate is strongly consistent and asymptotically normal.
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Original Russian Text © O.V. Shestakov, 2018, published in Vestnik Moskovskogo Universiteta, Seriya 15: Vychislitel’naya Matematika i Kibernetika, 2018, No. 2, pp. 36–39.
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Shestakov, O.V. Limit Theorems for Risk Estimate in Models with Non-Gaussian Noise. MoscowUniv.Comput.Math.Cybern. 42, 85–88 (2018). https://doi.org/10.3103/S027864191802005X
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DOI: https://doi.org/10.3103/S027864191802005X