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2020 Nonparametric regression with parametric help
Young K. Lee, Enno Mammen, Jens P. Nielsen, Byeong U. Park
Electron. J. Statist. 14(2): 3845-3868 (2020). DOI: 10.1214/20-EJS1760


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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Young K. Lee. Enno Mammen. Jens P. Nielsen. Byeong U. Park. "Nonparametric regression with parametric help." Electron. J. Statist. 14 (2) 3845 - 3868, 2020.


Received: 1 February 2020; Published: 2020
First available in Project Euclid: 21 October 2020

zbMATH: 07270279
MathSciNet: MR4164866
Digital Object Identifier: 10.1214/20-EJS1760

Primary: 62G08 , 62G20

Keywords: bias , cross-validatory bandwidth selectors , local linear estimation , profiling technique , regression function


Vol.14 • No. 2 • 2020
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