Data-driven discontinuity detection in derivatives of a regression function
(2004) Communications in Statistics: Theory and Methods — Vol. 33, n° 4, p. 851-871 (2004)
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- Abstract
- 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.
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Gijbels, I., & Goderniaux, A. (2004). Data-driven discontinuity detection in derivatives of a regression function. Communications in Statistics: Theory and Methods, 33(4), 851-871. https://doi.org/10.1081/STA-120028730 (Original work published 2004)