Testing discontinuities in nonparametric regression

Type
Article

Authors
Dai, Wenlin
Zhou, Yuejin
Tong, Tiejun

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Online Publication Date
2017-01-19

Print Publication Date
2018-02-17

Date
2017-01-19

Abstract
In nonparametric regression, it is often needed to detect whether there are jump discontinuities in the mean function. In this paper, we revisit the difference-based method in [13 H.-G. Müller and U. Stadtmüller, Discontinuous versus smooth regression, Ann. Stat. 27 (1999), pp. 299–337. doi: 10.1214/aos/1018031100]] and propose to further improve it. To achieve the goal, we first reveal that their method is less efficient due to the inappropriate choice of the response variable in their linear regression model. We then propose a new regression model for estimating the residual variance and the total amount of discontinuities simultaneously. In both theory and simulation, we show that the proposed variance estimator has a smaller mean-squared error compared to the existing estimator, whereas the estimation efficiency for the total amount of discontinuities remains unchanged. Finally, we construct a new test procedure for detection of discontinuities using the proposed method; and via simulation studies, we demonstrate that our new test procedure outperforms the existing one in most settings.

Citation
Dai W, Zhou Y, Tong T (2017) Testing discontinuities in nonparametric regression. Journal of Applied Statistics: 1–24. Available: http://dx.doi.org/10.1080/02664763.2017.1280004.

Acknowledgements
Tiejun Tong’s research was supported by the Hong Kong Baptist University grants FRG1/14-15/044, FRG2/15-16/019 and FRG2/15-16/038, and the National Natural Science Foundation of China grant (No. 11671338).

Publisher
Informa UK Limited

Journal
Journal of Applied Statistics

DOI
10.1080/02664763.2017.1280004

Additional Links
http://www.tandfonline.com/doi/full/10.1080/02664763.2017.1280004

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