Nonparametric Pointwise Estimation for a Regression Model with Multiplicative Noise
In this paper, we consider a general nonparametric regression estimation model with the feature of having multiplicative noise. We propose a linear estimator and nonlinear estimator by wavelet method. The convergence rates of those regression estimators under pointwise error over Besov spaces are pr...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/1599286 |
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| _version_ | 1849397502887854080 |
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| author | Jia Chen Junke Kou |
| author_facet | Jia Chen Junke Kou |
| author_sort | Jia Chen |
| collection | DOAJ |
| description | In this paper, we consider a general nonparametric regression estimation model with the feature of having multiplicative noise. We propose a linear estimator and nonlinear estimator by wavelet method. The convergence rates of those regression estimators under pointwise error over Besov spaces are proved. It turns out that the obtained convergence rates are consistent with the optimal convergence rate of pointwise nonparametric functional estimation. |
| format | Article |
| id | doaj-art-ae03f97d88f044e1ad8c88254c43df0f |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-ae03f97d88f044e1ad8c88254c43df0f2025-08-20T03:38:59ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/15992861599286Nonparametric Pointwise Estimation for a Regression Model with Multiplicative NoiseJia Chen0Junke Kou1School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, ChinaSchool of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, ChinaIn this paper, we consider a general nonparametric regression estimation model with the feature of having multiplicative noise. We propose a linear estimator and nonlinear estimator by wavelet method. The convergence rates of those regression estimators under pointwise error over Besov spaces are proved. It turns out that the obtained convergence rates are consistent with the optimal convergence rate of pointwise nonparametric functional estimation.http://dx.doi.org/10.1155/2021/1599286 |
| spellingShingle | Jia Chen Junke Kou Nonparametric Pointwise Estimation for a Regression Model with Multiplicative Noise Journal of Function Spaces |
| title | Nonparametric Pointwise Estimation for a Regression Model with Multiplicative Noise |
| title_full | Nonparametric Pointwise Estimation for a Regression Model with Multiplicative Noise |
| title_fullStr | Nonparametric Pointwise Estimation for a Regression Model with Multiplicative Noise |
| title_full_unstemmed | Nonparametric Pointwise Estimation for a Regression Model with Multiplicative Noise |
| title_short | Nonparametric Pointwise Estimation for a Regression Model with Multiplicative Noise |
| title_sort | nonparametric pointwise estimation for a regression model with multiplicative noise |
| url | http://dx.doi.org/10.1155/2021/1599286 |
| work_keys_str_mv | AT jiachen nonparametricpointwiseestimationforaregressionmodelwithmultiplicativenoise AT junkekou nonparametricpointwiseestimationforaregressionmodelwithmultiplicativenoise |