The role of pseudo data for robust smoothing with application to wavelet regression

Biometrika

Volumn 94, Issue 4, 2007, Pages 893-904

  Oh, Hee Seok ^a   Nychka, Douglas W ^b   Lee, Thomas C M ^c  

^a Seoul National University   (South Korea)

^b NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

^c CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Es algorithm; M estimation; Penalized least squares; Pseudo data; Robust smoothing; Wavelets

Indexed keywords

EID: 37549035459     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asm064     Document Type: Article

References (25)

1. ADAMS, R. (1975). Sobolev Spaces. New York: Academic Press.
2. 2 norms with application to Bayesian estimation. IEEE Trans. Sig. Proces. 42, 618-27.
3. ANGELINI, C., DE CANDITIIS, D. & LEBLANC, F. (2003). Wavelet regression estimation in non parametric mixed effect models. J. Mult. Anal. 85, 267-91.
4. ANTONIADIS, A. (1996). Smoothing noisy data with tapered Coiflets series. Scand. J. Statist. 23, 313-30.
5. ANTONIADIS, A. & FAN, J. (2001). Regularization of wavelet approximations. J. Am. Statist. Assoc. 96, 939-62.
6. AUBIN, J.-P. (2000). Applied Functional Analysis, 2nd ed. New York: Wiley.
7. AVERKAMP, R. & HOUDRÉ, C. (2003). Wavelets thresholding for non-necessarily Gaussian noise: Idealism. Ann. Statist. 31, 110-51.
8. CANTONI, E. & RONCHETTI, E. (2001). Resistant selection of the smoothing parameter for smoothing splines. Statist. Comp. 11, 141-6.
9. COX, D. D. (1983). Asymptotics for M-type smoothing splines. Ann. Statist. 11, 530-51.
10. DONOHO, D. L. & JOHNSTONE, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81, 425-55.
11. DONOHO, D. L., JOHNSTONE, I. M., HOCH, J. C. & STERN, A. S. (1992). Maximum entropy and the nearly black object (with Discussion). J. R. Statist. Soc. B 54, 41-81.
12. EILERS, P. H. C. & MARX, B. D. (1996). Flexible smoothing with B-splines and penalties (with Discussion). Statist. Sci. 11, 89-121.
13. HALL, P. & JONES, M. C. (1990). Adaptive M-estimation in nonparametric regression. Ann. Statist. 18, 1712-28.
14. HÄRDLE, W & GASSER, T (1984). Robust non-parametric function fitting. J. R. Statist. Soc. B 46, 42-51.
15. HUBER, P. J. (1973). Robust regression: asymptotics, conjectures and Monte Carlo. Ann. Statist. 1, 799-821.
16. HUBER, P. J. (1979). Robust smoothing. In Robustness in Statistics, Ed. R. L. Launer and G. N. Wilkinson, pp. 38-48. New York: Academic Press.
17. HUBER, P. J. (1981). Robust Statistics. New York: Wiley.
18. JOHNSTONE, I. M. & SILVERMAN, B. W. (2005). Empirical Bayes selection of wavelet thresholds. Ann. Statist. 33, 1700-52.
19. KOVAC, A. & SILVERMAN, B. W. (2000). Extending the scope of wavelet regression methods by coefficient-dependent thresholding. J. Am. Statist. Assoc. 95, 172-83.
20. MESSER, K. (1991). A comparison of a spline estimate to its equivalent kernel estimate. Ann. Statist. 19, 817-29.
21. NASON, G. P. (1998). WaveThres3 Software. Bristol, UK: Department of Mathematics, University of Bristol.
22. NYCHKA, D. W (1995). Splines as local smoothers. Ann. Statist. 23, 1175-97.
23. SARDY, S., TSENG, P. & BRUCE, A. (2001). Robust wavelet denoising. IEEE Trans. Sig. Proces. 49, 1146-52.
24. SILVERMAN, B. W. (1985). Some aspects of the spline smoothing approach to non-parametric regression curve fitting (with Discussion). J. R. Statist. Soc. B 47, 1-52.
25. SIMONOFF, J. S. (1996). Smoothing Methods in Statistics. New York: Springer.