A simple bootstrap bandwidth selector for local polynomial fitting

Abstract

A new, fully data-driven bandwidth selector with a double smoothing (DS) bias term and a data-driven variance estimator is developed following the bootstrap idea. The data-driven variance estimation does not involve any additional bandwidth selection. The proposed bandwidth selector convergences faster than a plug-in one due to the DS bias estimate, whereas the data-driven variance improves its finite sample performance clearly and makes it stable. Asymptotic results of the proposals are obtained. A comparative simulation study was done to show the overall gains and the gains obtained by improving either the bias term or the variance estimate, respectively. It is shown that the use of a good variance estimator is more important when the sample size is relatively small.

Keywords:

• bandwidth selection
• bootstrap
• double smoothing
• Rice criterion
• data-driven variance estimation
• local polynomial fitting

Acknowledgements

This work was supported in part by the Maxwell Institute for Mathematical Sciences, Heriot-Watt University. We would like to thank the Editor, the Associate Editor and a referee for their useful comments and suggestions which helped to improve the quality of the paper.