The Annals of Statistics

Automatic bandwidth choice and confidence intervals in nonparametric regression

Michael H. Neumann

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 15 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1034713641

Digital Object Identifier
doi:10.1214/aos/1034713641

Mathematical Reviews number (MathSciNet)
MR1389859

Zentralblatt MATH identifier
0856.62042

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

Keywords
Nonparametric regression bandwidth choice confidence intervals Edgeworth expansions

Citation

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. https://projecteuclid.org/euclid.aos/1034713641


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