Abstract

Data-driven discontinuity detection in derivatives of a regression function

GIJBELS, I. and A.-C. GODERNIAUX

This paper provides a fully data-driven procedure for estimating the locations of jump discontinuities occuring in the kth derivative of an unknown regression funtion. The basic ingredients for the procedure are a two-step method for estimating the locations of the jump discontinuities, a bootstrap procedure for selecting the smoothing parameters involved in this estimation and a cross-validation method for estimating the number of discontinuities in a derivative funtion. The paper extends ideas developed for change point detection in the regression function itself by Gijbels and Goderniaux {Gijbels, I., Goderniaux, A.-C. (2004). Bandwidth selection for change point estimation in nonparametric regression. Technometrics 46, 76-86}. A simulation study illustrates the performance of the procedure and applications to some real data demonstrate its use.

  Last update: June 30, 2004  - Contact : S. Malali