Communications in statistics-theory and methods vol:33 issue:4 pages:851-871
This paper provides a fully data-driven procedure for estimating the locations of jump discontinuities occuring in the kth derivative of an unknown regression function. 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 function. 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.