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