Adaptive $M$-Estimation in Nonparametric Regression
Hall, Peter ; Jones, M. C.
Ann. Statist., Tome 18 (1990) no. 1, p. 1712-1728 / Harvested from Project Euclid
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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.
Publié le : 1990-12-14
Classification:  Cross-validation,  Huber's $\psi$-function,  kernel estimation,  robust smoothing,  62G05,  62F35 
@article{1176347874,
     author = {Hall, Peter and Jones, M. C.},
     title = {Adaptive $M$-Estimation in Nonparametric Regression},
     journal = {Ann. Statist.},
     volume = {18},
     number = {1},
     year = {1990},
     pages = { 1712-1728},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176347874}
}

Hall, Peter; Jones, M. C. Adaptive $M$-Estimation in Nonparametric Regression. Ann. Statist., Tome 18 (1990) no. 1, pp.  1712-1728. http://gdmltest.u-ga.fr/item/1176347874/