Limit Theorems for Risk Estimate in Models with Non-Gaussian Noise |
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Authors: | Email author" target="_blank">O?V?ShestakovEmail author |
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Institution: | 1.Faculty of Computational Mathematics and Cybernetics,Moscow State University,Moscow,Russia;2.Institute of Informatics Problems, Federal Research Center “Computer Science and Control”,Russian Academy of Sciences,Moscow,Russia |
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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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