Wavelet Estimation of Function Derivatives from a Multichannel Deconvolution Model
This paper considers a multichannel deconvolution model with Gaussian white noises. The goal is to estimate the d-th derivatives of an unknown function in the model. For super-smooth case, we construct an adaptive linear wavelet estimator by wavelet projection method. For regular-smooth case, we pro...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/2075229 |
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| Summary: | This paper considers a multichannel deconvolution model with Gaussian white noises. The goal is to estimate the d-th derivatives of an unknown function in the model. For super-smooth case, we construct an adaptive linear wavelet estimator by wavelet projection method. For regular-smooth case, we provide an adaptive nonlinear wavelet estimator by hard-thresholded method. In order to measure the global performances of our estimators, we show upper bounds on convergence rates using the Lp-risk (1≤p<∞). |
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| ISSN: | 2314-8888 |