We study the estimation of a regression function by two classes of estimators, the Nadaraya-Watson Kernel type estimators and the orthogonal polynomial estimators. We obtain sharp pointwise rates of strong consistency by establishing laws of the iterated logarithm for the two classes of estimators. These results parallel those of Hall (1981) on density estimation and extend those of Noda (1976) on strong consistency of kernel regression estimators.
Publié le : 1984-06-14
Classification:
Nonparametric regression function estimation,
law of the iterated logarithm,
kernel estimation,
orthogonal polynomial estimation,
60F10,
60G15,
62G05
@article{1176346510,
author = {Hardle, Wolfgang},
title = {A Law of the Iterated Logarithm for Nonparametric Regression Function Estimators},
journal = {Ann. Statist.},
volume = {12},
number = {1},
year = {1984},
pages = { 624-635},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346510}
}
Hardle, Wolfgang. A Law of the Iterated Logarithm for Nonparametric Regression Function Estimators. Ann. Statist., Tome 12 (1984) no. 1, pp. 624-635. http://gdmltest.u-ga.fr/item/1176346510/