Abstract
A method for robust nonparametric regression is discussed. We consider kernel $M$-estimates of the regression function using Huber's $\psi$-function and extend results of Hardle and Gasser to the case of random designs. A practical adaptive procedure is proposed consisting of simultaneously minimising a cross-validatory criterion with respect to both the smoothing parameter and a robustness parameter occurring in the $\psi$-function. This method is shown to possess a theoretical asymptotic optimality property, while some simulated examples confirm that the approach is practicable.
Citation
Peter Hall. M. C. Jones. "Adaptive $M$-Estimation in Nonparametric Regression." Ann. Statist. 18 (4) 1712 - 1728, December, 1990. https://doi.org/10.1214/aos/1176347874
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