Frequentist optimality of Bayesian wavelet shrinkage rules for Gaussian and non-Gaussian noise
نویسندگان
چکیده
منابع مشابه
Frequentist Optimality of Bayesian Wavelet Shrinkage Rules for Gaussian and Non-gaussian Noise1 by Marianna Pensky
The present paper investigates theoretical performance of various Bayesian wavelet shrinkage rules in a nonparametric regression model with i.i.d. errors which are not necessarily normally distributed. The main purpose is comparison of various Bayesian models in terms of their frequentist asymptotic optimality in Sobolev and Besov spaces. We establish a relationship between hyperparameters, ver...
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Air pollution is one of the major problems of Tehran metropolis. Regarding the fact that Tehran is surrounded by Alborz Mountains from three sides, the pollution due to the cars traffic and other polluting means causes the pollutants to be trapped in the city and have no exit without appropriate wind guff. Carbon monoxide (CO) is one of the most important sources of pollution in Tehran air. The...
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Wavelet shrinkage and thresholding methods constitute a powerful way to carry out signal denoising, especially when the underlying signal has a sparse wavelet representation. They are computationally fast, and automatically adapt to the smoothness of the signal to be estimated. Nearly minimax properties for simple threshold estimators over a large class of function spaces and for a wide range o...
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For signals belonging to balls in smoothness classes and noise with enough moments, the asymptotic behavior of the minimax quadratic risk among soft–threshold estimates is investigated. In turn, these results combined with a median filtering method lead to asymptotics for denoising heavy tails via wavelet thresholding. Some further comparisons of wavelet thresholding and of kernel estimators ar...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2006
ISSN: 0090-5364
DOI: 10.1214/009053606000000128