On jump detection in regression curves using local polynomial kernel estimation

Pakistan Journal of Statistics

Volumn 25, Issue 4, 2009, Pages 505-528

  Zhang, Bo ^a   Su, Zhihua ^a   Qiu, Peihua ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Bandwidth selection; Bootstrap resampling; Consistency; Curve estimation; Discontinuities; Jumps; Local smoothing; Nonparametric regression

Indexed keywords

EID: 70849111550     PISSN: 10129367     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. Eubank, R.L., and Speckman, P.L. (1994), "Nonparametric estimation of functions with jump discontinuities," IMS Lecture Notes, 23, Change-Point Problems (E. Carlstein, H.G. Müller and D. Siegmund eds.), 130-144.
2. Grégoire, G., and Hamrouni, Z. (2002), "Change-point estimation by local linear smoothing," Journal of Multivariate Analysis, 83, 56-83.
3. Gijbels, I., and Goderniaux, A.-C. (2004), "Bandwidth selection for change point estimation in nonparametric regression," Technometrics, 46, 76-86.
4. Gijbels, I., Hall, P., and Kneip, A. (1999), "On the estimation of jump points in smooth curves," The Annals of the Institute of Statistical Mathematics, 51, 231-251.
5. Gijbels, I., Lambert, A., and Qiu, P. (2007), "Jump-preserving regression and smoothing using local linear fitting: a compromise," Annals of the Institute of Statistical Mathematics, 59, 235-272.
6. Hall, P., and Titterington, M. (1992), "Edge-preserving and peak-preserving smoothing," Technometrics, 34, 429-440.
7. Joo, J., and Qiu, P. (2009), "Jump detection in a regression curve and its derivative," Technometrics, in press.
8. Loader, C.R. (1996), "Change point estimation using nonparametric regression," The Annals of Statistics, 24, 1667-1678.
9. Müller, Ch.H.(2002),"Robustestimatorsforestimatingdiscontinuousfunctions,"Metrika, 55, 99-109.
10. Müller, H.G. (1992 "Change-points in nonparametric regression analysis," The Annals of Statistics, 20, 737-761.
11. Qiu, P. (1991), "Estimation of a kind of jump regression functions," Systems Science and Mathematical Sciences, 4, 1-13.
12. Qiu, P. (1994), "Estimation of the number of jumps of the jump regression functions," Communications in Statistics-Theory and Methods, 23, 2141-2155.
13. Qiu, P. (1999), "Comparisonsof severallocal smoothing jump detectors in one-dimensional nonparametric regression," The ASA Proceedings of the Statistical Computing Section, 150-155.
14. Qiu, P. (2003), "A jump-preservingcurve fitting procedurebased on local piecewise-linear kernel estimation," Journal of Nonparametric Statistics, 15, 437-453.
15. Qiu, P. (2005), Image Processing and Jump Regression Analysis, New York: John Wiley & Sons.
16. Qiu, P., Asano, Chi., and Li, X. (1991), "Estimation of jump regression functions," Bulletin of Informatics and Cybernetics, 24, 197-212.
17. Qiu, P., and Yandell, B. (1998), "A local polynomial jump detection algorithm in nonparametric regression," Technometrics, 40, 141-152.
18. Shiau, J. (1987), "A note on MSE coverage intervals in a partial Spline model," Communications in Statistics - Theory and Methods, 16, 1851-1866.
19. Wang, Y. (1995), "Jump and sharp cusp detection by wavelets," Biometrika, 82, 385-397.
20. Wu, J.S., and Chu, C.K. (1993), "Kernel type estimators of jump points and values of a regression function," The Annals of Statistics, 21, 1545-1566.
21. Wu, W.B., and Zhao, Z. (2007), "Inference of trends in time series," Journal of the Royal Statistical Society (Series B), 69, 391-410.