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December 1995 Automatic bandwidth choice and confidence intervals in nonparametric regression
Michael H. Neumann
Ann. Statist. 23(6): 1937-1959 (December 1995). DOI: 10.1214/aos/1034713641


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.


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Michael H. Neumann. "Automatic bandwidth choice and confidence intervals in nonparametric regression." Ann. Statist. 23 (6) 1937 - 1959, December 1995.


Published: December 1995
First available in Project Euclid: 15 October 2002

zbMATH: 0856.62042
MathSciNet: MR1389859
Digital Object Identifier: 10.1214/aos/1034713641

Primary: 62G15
Secondary: 62G07, 62G20

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 6 • December 1995
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