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标题：A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under <svg style="vertical-align:-0.216pt;width:12.8625px;" id="M1" height="10.4375" version="1.1" viewBox="0 0 12.8625 10.4375" width="12.8625" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.022,-0,0,-.022,.062,10.1)"><path id="x1D6FC" d="M545 106q-67 -118 -134 -118q-24 0 -40 37.5t-30 129.5h-2q-47 -72 -103 -119.5t-108 -47.5q-47 0 -76 45.5t-29 119.5q0 113 85 204t174 91q47 0 70 -33.5t43 -119.5h3q32 47 80 140l55 13l10 -9q-47 -80 -138 -201q17 -99 27.5 -136t22.5 -37q23 0 69 61zM333 204
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作者：Christophe Chesneau
期刊名称：Journal of Probability and Statistics
印刷版ISSN：1687-952X
电子版ISSN：1687-9538
出版年度：2014
卷号：2014
DOI：10.1155/2014/403764
出版社：Hindawi Publishing Corporation
摘要：We consider the estimation of an unknown function for weakly dependent data (-mixing) in a general setting. Our contribution is theoretical: we prove that a hard thresholding wavelet estimator attains a sharp rate of convergence under the mean integrated squared error (MISE) over Besov balls without imposing too restrictive assumptions on the model. Applications are given for two types of inverse problems: the deconvolution density estimation and the density estimation in a GARCH-type model, both improve existing results in this dependent context. Another application concerns the regression model with random design.