A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence
We consider the estimation of an unknown function f for 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 with...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2014/403764 |
| Summary: | We consider the estimation of an unknown function f for 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. |
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| ISSN: | 1687-952X 1687-9538 |