The Annals of Statistics

Automatic bandwidth choice and confidence intervals in nonparametric regression

Michael H. Neumann

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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 information

Ann. Statist., Volume 23, Number 6 (1995), 1937-1959.

First available in Project Euclid: 15 October 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G15: Tolerance and confidence regions
Secondary: 62G07: Density estimation 62G20: Asymptotic properties

Nonparametric regression bandwidth choice confidence intervals Edgeworth expansions


Neumann, Michael H. Automatic bandwidth choice and confidence intervals in nonparametric regression. Ann. Statist. 23 (1995), no. 6, 1937--1959. doi:10.1214/aos/1034713641.

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