Spline estimation of discontinuous regression functions

Journal of Computational and Graphical Statistics

Volumn 6, Issue 3, 1997, Pages 266-284

  Koo, Ja Yong ^a  

^a Hallym University   (South Korea)

Author keywords

Basis selection; BIC; Change point; Discontinuity; Knot merging; Multiple knots; Regression functions; Splines; Stepwise basis deletion; Stepwise knot addition

Indexed keywords

EID: 0031313446     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.1997.10474742     Document Type: Article

References (27)

1. Altman, N. S. (1990), “Kemel Smoothing of Data With Correlated Errors,” Journal of the American Statistical Association, 85, 749-759.
2. de Boor, C. (1978), A Practical Guide to Splines, New York: Springer-Verlag.
3. Breiman, L. (1993), “Fitting Additive Models to Regression Data: Diagnostics and Alternative Views,” Computational Statistics and Data Analysis, 15, 13-46.
4. Breiman, L., and Peters, S. (1992), “Comparing Automatic Smoothers (a public service enterprise),” International Statistical Review, 60, 271-290.
5. Carlstein, E., Müller, H. G., and Siegmund, D. (1994), Change-Point Problems, Lecture Notes-Monograph Series, Vol. 23, Hayward, CA: Institute of Mathematical Statistics.
6. Cobb, G. W. (1978), “The Problem of the Nile: Conditional Solution to a Changepoint Problem,” Biometrika, 65, 243-251.
7. Donoho, D. L. (1994), “On Minimum Entropy Segmentation,” in Wavelets: Theory, Algorithms, and Applications, ed. C. K. Chui, L. Montefusco, and L. Puccio, San Diego, CA: Academic Press.
8. Donoho, D. L., and Johnstone, I. M. (1994), "Ideal Spatial Adaptation by Wavelet Shrinkage,” Biometrika, 81, 425-455.
9. Friedman, J. H. (1991), “Multivariate Adaptive Regression Splines” (with discussion), The Annals of Statistics, 19, 1-141.
10. Friedman, J. H., and Silverman, B. W. (1989), “Flexible Parsimonious Smoothing and Additive Modeling,” Technometrics, 31, 3-39.
11. Gordon, K., and Smith, A. F. (1990), “Modeling and Monitoring Biomedical Time Series,” Journal of the American Statistical Association, 85, 328-337.
12. Hall, P., and Titterington, D. M. (1992), “Edge-Preserving and Peak-Preserving Smoothing,” Technometrics, 34, 429-140.
13. Hinkley, D. V. (1969), “Inference About the Intersection in Two-Phase Regression,” Biometrika, 56, 495-504.
14. Hinkley, D. V. (1971), “Inference in Two-Phase Regression,” Journal of the American Statistical Association, 66, 736-743.
15. Koo, J.-Y., and Lee, Y. (1994), “Bivariate B-Splines in Generalized Linear Models,” Journal of Statistical Computation and Simulations, 50, 119-129.
16. Lombard, F. (1988), “Detecting Change Points by Fourier Analysis,” Technometrics, 30, 305-310.
17. Mallat, S. G., and Hwang, W. L. (1992), “Singularity Detection and Processing With Wavelets,” IEEE Transaction on Information Theory, 38, 617-643.
18. McDonald, J. A., and Owen, A. B. (1986), “Smoothing With Split Linear Fits,” Technometrics, 28, 195-208.
19. Müller, H. G. (1992), “Change-Points in Nonparametric Regression Analysis,” The Annals of Statistics, 20, 737-761.
20. Nason, G. P., and Silverman, B. W. (1994), “The Discrete Wavelet Transform in S,” Journal Computational and Graphical Statistics, 3, 163-191.
21. Press, W. H., Teukolsky, S. A., Vetterling, W. T„ and Flannery, B. P. (1992), Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd Ed., New York: Cambridge University Press.
22. Schwarz, G. (1978), “Estimating the Dimension of a Model,” The Annals of Statistics, 6, 461-464.
23. Seber, G. A. F. (1977), “Linear Regression Analysis,” New York: John Wiley and Sons.
24. Stone, C. J. (1985), “Additive Regression and Other Nonparametric Models,” The Annals of Statistics, 13, 689-705.
25. Wang, Y. (1995), “Jump and Sharp Cusp Detection by Wavelets,” Biometrika, 82, 385-397.
26. Yin, Y. Q. (1988), “Detection of the Number, Locations and Magnitudes of Jumps,” Communications in Statistics, Stochastic Models, 4, 445-455.
27. Zhang, H. (1994), “Maximal Correlation and Adaptive Splines,” Technometrics, 36, 196-201.