Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors
A new variable bandwidth selector for kernel estimation is proposed. The application of this bandwidth selector leads to kernel estimates that achieve optimal rates of convergence over Besov classes. This implies that the procedure adapts to spatially inhomogeneous smoothness. In particular, the est...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1997
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| In: |
The annals of statistics
Year: 1997, Volume: 25, Issue: 3, Pages: 929-947 |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/aos/1069362731 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1214/aos/1069362731 Verlag, Volltext: https://projecteuclid.org/euclid.aos/1069362731 Verlag, Volltext: https://projecteuclid.org/download/pdf_1/euclid.aos/1069362731 
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| Author Notes: | O.V. Lepski, E. Mammen, V.G. Spokoiny |
| Summary: | A new variable bandwidth selector for kernel estimation is proposed. The application of this bandwidth selector leads to kernel estimates that achieve optimal rates of convergence over Besov classes. This implies that the procedure adapts to spatially inhomogeneous smoothness. In particular, the estimates share optimality properties with wavelet estimates based on thresholding of empirical wavelet coefficients. |
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| Item Description: | First available in Project Euclid: 20 November 2003 Gesehen am 15.02.2018 |
| Physical Description: | Online Resource |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/aos/1069362731 |