A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator underα-Mixing Dependence
2014 ◽
Vol 2014
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pp. 1-12
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Keyword(s):
The Mean
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We consider the estimation of an unknown functionffor weakly dependent data (α-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.
2016 ◽
Vol 5
(2)
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pp. 35
2011 ◽
Vol 09
(06)
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pp. 989-1023
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Keyword(s):
2001 ◽
Vol 52
(4)
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pp. 441-450
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2011 ◽
Vol 09
(04)
◽
pp. 587-609
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1986 ◽
Vol 18
(1)
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pp. 150-168
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1993 ◽
Vol 45
(1)
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pp. 137-160
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