Weak laws of large numbers and central limit theorems are proved for integrated square error of kernel estimators of regression functions. The regressor is assumed to take values in $\mathbb{R}^p$, and the regressand, $X$, to be real valued. It is shown that in many cases, integrated square error is asymptotically normally distributed and independent of the $X$-sample. As an application, a test for the regression function (such as that proposed by Konakov) is seen to be asymptotically independent of an arbitrary test based on the $X$-sample. The proofs involve martingale methods.
Publié le : 1984-03-14
Classification:
Central limit theorem,
integrated square error,
kernel estimator,
law of large numbers,
multivariate,
nonparametric,
regression,
test for regression,
62G20,
62E20,
60F05
@article{1176346404,
author = {Hall, Peter},
title = {Integrated Square Error Properties of Kernel Estimators of Regression Functions},
journal = {Ann. Statist.},
volume = {12},
number = {1},
year = {1984},
pages = { 241-260},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346404}
}
Hall, Peter. Integrated Square Error Properties of Kernel Estimators of Regression Functions. Ann. Statist., Tome 12 (1984) no. 1, pp. 241-260. http://gdmltest.u-ga.fr/item/1176346404/