In the present paper we combine the issues of bandwidth choice and construction of confidence intervals in nonparametric regression. Main emphasis is put on fully data-driven methods. We modify the $\sqrt{n}$-consistent bandwidth selector of Härdle, Hall and Marron such that it is appropriate for heteroscedastic data, and we show how one can optimally choose the bandwidth g of the pilot estimator $\hat{m}_g$. Then we consider classical confidence intervals based on kernel estimators with data-driven bandwidths and compare their coverage accuracy. We propose a method to put undersmoothing with a data-driven bandwidth into practice and show that this procedure outperforms explicit bias correction.
@article{1034713641,
author = {Neumann, Michael H.},
title = {Automatic bandwidth choice and confidence intervals in nonparametric regression},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 1937-1959},
language = {en},
url = {http://dml.mathdoc.fr/item/1034713641}
}
Neumann, Michael H. Automatic bandwidth choice and confidence intervals in nonparametric regression. Ann. Statist., Tome 23 (1995) no. 6, pp. 1937-1959. http://gdmltest.u-ga.fr/item/1034713641/