Bootstrap test for change-points in nonparametric regression

Journal of Nonparametric Statistics

Volumn 16, Issue 3-4, 2004, Pages 591-611

  Gijbels, I ^a   Goderniaux, A C ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Bandwidth; Bootstrap; Cross validation; Derivative; Discontinuity points; Least squares fitting; Local polynomial approximation

Indexed keywords

EID: 1542535008     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485250310001626088     Document Type: Conference Paper

References (41)

1. Antoniadis, A. and Gijbels, I. (2002). Detecting abrupt changes by wavelet methods. Journal of Nonparametric Statistics, 14, 7-29.
2. Bowman, A. W., Jones, M. C. and Gijbels, I. (1998). Testing monotonicity of regression. Journal of Computational and Graphical Statistics, 7, 489-500.
3. Chu, C. K. (1994). Estimation of change-points in a nonparametric regression function through kernel density estimation. Communications in Statistics, Part A - Theory and Methods, 23, 3037-3062.
4. Cline, D.B.H., Eubank, R. and Speckman, P. (1995). Nonparametric estimation of regression curves with discontinuous derivatives. Journal of Statistical Research, 29, 17-30.
5. Cobb, G. W. (1978). The problem of the Nile: conditional solution to a change-point problem. Biometrika, 62, 243-251.
6. Dubowik, Ch. and Stadtmüller, U. (2000). Detecting jumps in nonparametric regression. In: Asymptotics in Statistics and Probability, Ed. Puri, M. L. pp 171-184.
7. Eubank, R. L. and Speckman, P.L. (1994). Nonparametric estimation of functions with jump discontinuities. In: Change-point Problems, Eds. Carlstein, E., Müller, H.-G., and Siegmund, D. IMS-Lecture Notes, Vol. 23, 130-143.
8. Fan, J. and Gijbels, I. (1996). Local Polynomial Modelling and its Applications. Chapman and Hall, New York.
9. Gijbels, I. and Goderniaux, A-C. (2004a). Bandwidth selection for change point estimation in nonparametric regression. Technometrics, 46, 76-86.
10. Gijbels, I. and Goderniaux, A-C. (2004b). Data-driven discontinuity detection in derivatives of a regression function. Communications in Statistics, Part A -Theory and Methods, 33, 851-871.
11. 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.
12. Gijbels, I., Hall, P. and Kneip, A. (2003). Interval and band estimation for curves with jumps. Journal of Applied Probability. (Special Issue in honour of Chris Heyde), (to appear.).
13. Grégoire, G. and Hamrouni, Z. (2002a). Change-point estimation by local linear smoothing. Journal of Multivariate Analysis, 83, 56-83.
14. Grégoire, G. and Hamrouni, Z. (2002b). Two nonparametric tests for change-point problem. Journal of Nonparametric Statistics, 14, 87-112.
15. Hall, P. and Titterington, D. M. (1992). Edge preserving and peak-preserving smoothing. Technometrics, 34, 429-440.
16. Hamrouni, Z. (1999). Inférence statistique par lissage linéaire local pour une fonction de régression présentant des discontinuités. Doctoral thesis, Université de Joseph Fourier, Grenoble, France.
17. Härdle, W. (1990). Applied Nonparametric Regression. Econometric Society Monograph Series Vol. 19, Cambridge University Press.
18. Harezlak, J. (1998). Bump hunting revisited. MSc thesis, Department of Statistics, University of British Columbia, Vancouver, Canada.
19. Harezlak, J. and Heckman, N. (2001). Crisp: a tool in bump hunting. Journal of Computational and Graphical Statistics, 10, 713-729.
20. Horváth, L. and Kokoszka, P. (1997). Change-point detection with nonparametric regression. Technical report, University of Liverpool.
21. Horváth, L. and Kokoszka, P. (2002). Change-point detection with non-parametric regression. Statistics, 36, 9-31.
22. Jarrett, R. G. (1979). A note on the intervals between coal-mining disasters. Biometrika, 66, 191-193.
23. Loader, C. R. (1996). Change point estimation using nonparametric regression. The Annals of Statistics, 24, 1667-1678.
24. McDonald, J. A. and Owen, A. B. (1986), Smoothing with split linear fits. Technometrics, 28, 195-208.
25. Müller, H.-G. (1992). Change-points in nonparametric regression analysis. The Annals of Statistics, 20, 737-761.
26. Müller, H.-G. and Song, K.-S. (1997). Two-stage change-point estimators in smooth regression models. Statistics & Probability Letters, 34, 323-335.
27. Müller, H.-G. and Stadtmüller, U. (1999). Discontinuous versus smooth regression. The Annals of Statistics, 27, 299-337.
28. Müller, H.-G., Stadtmüller, U. and Schmitt, T. (1987). Bandwidth choice and confidence intervals for derivatives of noisy data. Biometrika, 74, 4, 743-749.
29. Nadaraya, E. A. (1964). On estimating regression. Theory of Probability and Applications, 9, 141-142.
30. Qiu, P. and Yandell, B. (1998). A local polynomial jump-detection algorithm in nonparametric regression. Technometrics, 40, 141-152.
31. Raimondo, M. (1998). Minimax estimation of sharp change points. The Annals of Statistics, 26, 1379-1397.
32. Scott, D. W. (1992). Multivariate Density Estimation. Theory, Practice and Visualization. Wiley, New York.
33. Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.
34. Speckman, P. L. (1994). Detection of change-points in nonparametric regression, (unpublished manuscript.)
35. Speckman, P. L. (1995). Fitting curves with features: semiparametric change-point methods. Computing science and statistics, 26, 257-264.
36. Spokoiny, V. G. (1998). Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice. The Annals of Statistics, 26, 1356-1378.
37. Wang, Y. (1995). Jump and sharp cusp detection by wavelets. Biometrika, 82, 385-397.
38. Watson, G. S. (1964). Smooth regression analysis. Sankhyā Series A, 26, 359-372.
39. Wu, J. S. and Chu, C. K. (1993a). Kernel type estimation of jump points and values of regression function. The Annals of Statistics, 21, 1545-1566.
40. Wu, J. S. and Chu, C. K. (1993b). Modification for boundary effects and jump points in nonparametric regression. Nonparametric Statistics, 2, 341-354.
41. Wu, J. S. and Chu, C. K. (1993c). Nonparametric function estimation and bandwidth selection for discontinuous regression functions. Statistica Sinica, 3, 557-576.