Bootstrap test for change-points in nonparametric regression

Abstract

The objective of this article is to test whether or not there is an abrupt change in the regression function itself or in its first derivative at certain (prespecified or not) locations. The test does not rely on asymptotics but approximates the sample distribution of the test statistic using a bootstrap procedure. The proposed testing method involves a data-driven choice of the smoothing parameters. The performance of the testing procedures is evaluated via a simulation study. Some comparison with an asymptotic test by Hamrouni (1999) and Grégoire and Hamrouni (2002b) and asymptotic tests by Müller and Stadtmüller (1999) and Dubowik and Stadtmüller (2000) is provided. We also demonstrate the use of the testing procedures on some real data.

Keywords:

• Bandwidth
• Bootstrap
• Cross-validation
• Discontinuity points
• Derivative
• Least-squares fitting
• Local polynomial approximation

Acknowledgements

The authors thank Professor Ulrich Stadtmüller for making them aware of the work by Dubowik and Stadtmüller. The authors also owe thanks to an anonymous referee for careful reading of the first version of the manuscript. Financial support from the contract ’Projet d’Actions de Recherche Concertées’ nr 98/03-217 from the Belgian government, and from the lAP research network nr P5/24 of the Belgian State (Federal Office for Scientific, Technical and Cultural Affairs) is gratefully acknowledged.