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 |
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Wiley
2014-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2014/403764 |
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| _version_ | 1832561885530030080 |
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| author | Christophe Chesneau |
| author_facet | Christophe Chesneau |
| author_sort | Christophe Chesneau |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-032bf678aa104bb98573247f5ff36ad1 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-032bf678aa104bb98573247f5ff36ad12025-02-03T01:23:50ZengWileyJournal of Probability and Statistics1687-952X1687-95382014-01-01201410.1155/2014/403764403764A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing DependenceChristophe Chesneau0Laboratoire de Mathéematiques Nicolas Oresme, Université de Caen, BP 5186, 14032 Caen Cedex, FranceWe 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.http://dx.doi.org/10.1155/2014/403764 |
| spellingShingle | Christophe Chesneau A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence Journal of Probability and Statistics |
| title | A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence |
| title_full | A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence |
| title_fullStr | A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence |
| title_full_unstemmed | A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence |
| title_short | A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence |
| title_sort | general result on the mean integrated squared error of the hard thresholding wavelet estimator under α mixing dependence |
| url | http://dx.doi.org/10.1155/2014/403764 |
| work_keys_str_mv | AT christophechesneau ageneralresultonthemeanintegratedsquarederrorofthehardthresholdingwaveletestimatorunderamixingdependence AT christophechesneau generalresultonthemeanintegratedsquarederrorofthehardthresholdingwaveletestimatorunderamixingdependence |