Nonparametric regression with parametric help
In this paper we propose a new nonparametric regression technique. Our proposal has common ground with existing two-step procedures in that it starts with a parametric model. However, our approach differs from others in the choice of parametric start within the parametric family. Our proposal choose...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
21 October 2020
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| In: |
Electronic journal of statistics
Year: 2020, Volume: 14, Issue: 2, Pages: 3845-3868 |
| ISSN: | 1935-7524 |
| DOI: | 10.1214/20-EJS1760 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1214/20-EJS1760 Verlag, lizenzpflichtig, Volltext: https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-14/issue-2/Nonparametric-regression-with-parametric-help/10.1214/20-EJS1760.full 
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| Author Notes: | Young K. Lee, Enno Mammen, Jens P. Nielsen and Byeong U. Park |
| Summary: | In this paper we propose a new nonparametric regression technique. Our proposal has common ground with existing two-step procedures in that it starts with a parametric model. However, our approach differs from others in the choice of parametric start within the parametric family. Our proposal chooses a function that is the projection of the unknown regression function onto the parametric family in a certain metric, while the existing methods select the best approximation in the usual $L_{2}$ metric. We find that the difference leads to substantial improvement in the performance of regression estimators in comparison with direct one-step estimation, irrespective of the choice of a parametric model. This is in contrast with the existing two-step methods, which fail if the chosen parametric model is largely misspecified. We demonstrate this with sound theory and numerical experiment. |
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| Item Description: | Gesehen am 07.06.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1935-7524 |
| DOI: | 10.1214/20-EJS1760 |