Pointwise Wavelet Estimations for a Regression Model in Local Hölder Space
This paper considers an unknown functional estimation problem in a regression model with multiplicative and additive noise. A linear wavelet estimator is first constructed by a wavelet projection operator. The convergence rate under the pointwise error of linear wavelet estimators is studied in loca...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/9/466 |
| _version_ | 1797491186232983552 |
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| author | Junke Kou Qinmei Huang Huijun Guo |
| author_facet | Junke Kou Qinmei Huang Huijun Guo |
| author_sort | Junke Kou |
| collection | DOAJ |
| description | This paper considers an unknown functional estimation problem in a regression model with multiplicative and additive noise. A linear wavelet estimator is first constructed by a wavelet projection operator. The convergence rate under the pointwise error of linear wavelet estimators is studied in local Hölder space. A nonlinear wavelet estimator is provided by the hard thresholding method in order to obtain an adaptive estimator. The convergence rate of the nonlinear estimator is the same as the linear estimator up to a logarithmic term. Finally, it should be pointed out that the convergence rates of two wavelet estimators are consistent with the optimal convergence rate on pointwise nonparametric estimation. |
| first_indexed | 2024-03-10T00:43:51Z |
| format | Article |
| id | doaj.art-1a4dd8fdac724af18470a8ac50211b86 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T00:43:51Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-1a4dd8fdac724af18470a8ac50211b862023-11-23T15:02:31ZengMDPI AGAxioms2075-16802022-09-0111946610.3390/axioms11090466Pointwise Wavelet Estimations for a Regression Model in Local Hölder SpaceJunke Kou0Qinmei Huang1Huijun Guo2School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, ChinaSchool of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, ChinaSchool of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, ChinaThis paper considers an unknown functional estimation problem in a regression model with multiplicative and additive noise. A linear wavelet estimator is first constructed by a wavelet projection operator. The convergence rate under the pointwise error of linear wavelet estimators is studied in local Hölder space. A nonlinear wavelet estimator is provided by the hard thresholding method in order to obtain an adaptive estimator. The convergence rate of the nonlinear estimator is the same as the linear estimator up to a logarithmic term. Finally, it should be pointed out that the convergence rates of two wavelet estimators are consistent with the optimal convergence rate on pointwise nonparametric estimation.https://www.mdpi.com/2075-1680/11/9/466nonparametric estimationpointwise errorlocal Hölder spacewavelet |
| spellingShingle | Junke Kou Qinmei Huang Huijun Guo Pointwise Wavelet Estimations for a Regression Model in Local Hölder Space Axioms nonparametric estimation pointwise error local Hölder space wavelet |
| title | Pointwise Wavelet Estimations for a Regression Model in Local Hölder Space |
| title_full | Pointwise Wavelet Estimations for a Regression Model in Local Hölder Space |
| title_fullStr | Pointwise Wavelet Estimations for a Regression Model in Local Hölder Space |
| title_full_unstemmed | Pointwise Wavelet Estimations for a Regression Model in Local Hölder Space |
| title_short | Pointwise Wavelet Estimations for a Regression Model in Local Hölder Space |
| title_sort | pointwise wavelet estimations for a regression model in local holder space |
| topic | nonparametric estimation pointwise error local Hölder space wavelet |
| url | https://www.mdpi.com/2075-1680/11/9/466 |
| work_keys_str_mv | AT junkekou pointwisewaveletestimationsforaregressionmodelinlocalholderspace AT qinmeihuang pointwisewaveletestimationsforaregressionmodelinlocalholderspace AT huijunguo pointwisewaveletestimationsforaregressionmodelinlocalholderspace |