Adaptive M-estimation in nonparametric regression

Hall, P. and Jones, Chris (1990). Adaptive M-estimation in nonparametric regression. Annals of Statistics, 18(4) pp. 1712–1728.

Abstract

A method for robust nonparametric regression is discussed. A method for robust nonparametric regression is discussed. We consider kernel M-estimates of the regression function using Huber's ψ-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 ψ-function. This method is shown to possess a theoretical asymptotic optimality property, while some simulated examples confirm that the approach is practicable.

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