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Nonparametric regression with parametric help

Lee, Y. K., Mammen, E., Nielsen, J. P. ORCID: 0000-0002-2798-0817 & Park, B. U. (2020). Nonparametric regression with parametric help. Electronic Journal of Statistics, 14(2), pp. 3845-3868. doi: 10.1214/20-EJS1760

Abstract

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 di↵ers 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 L2 metric. We find that the di↵erence 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.

Publication Type: Article
Publisher Keywords: Regression function, bias, profiling technique, local linear estimation, crossvalidatory, bandwidth selectors
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Departments: Bayes Business School > Actuarial Science & Insurance
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