Variable bandwidth and one-step local M-estimator

Science in China, Series A: Mathematics, Physics, Astronomy

Volumn 43, Issue 1, 2000, Pages 65-81

  Fan, Jianqing ^a   Jiang, Jiancheng ^b  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b PEKING UNIVERSITY   (China)

Author keywords

Local regression; M estimator; Nonparametric estimation; One step; Robustness; Variable bandwidth

Indexed keywords

EID: 0042689800     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02903849     Document Type: Article

References (19)

1. Fan, J., Gijbels, I., Local Polynomial Modelling and Its Applications, London: Chapman and Hall, 1996.
2. Härdle, W., Applied Nonparametric Regression, New York: Cambridge University Press, 1990.
3. Wand, M. P., Jones, M. C., Kernel Smoothing, London: Chapman and Hall, 1995.
4. Fan, J., Local linear regression smoothers and their minimax efficiencies, Ann. Statist., 1993, 21: 196.
5. Ruppert, D., Wand, M. P., Multivariate weighted least squares regression, Ann. Statist., 1994, 22: 1 346
6. Cleveland, W. S., Robust locally weighted regression and smoothing scatterplots, J. Amer. Statist. Assoc., 1979, 74: 829.
7. Cox, D. D., Asymptotics for M-type smoothing splines, Ann. Statist., 1983, 11: 530.
8. Tsybakov, A. B., Robust reconstruction of functions by the local-approximation method, Problems of Information Transmission, 1986, 22: 133.
9. Härdle, W., Tsybakov, A. B., Robust nonparametric regression with simultaneous scale curve estimation, Ann. Statist., 1988, 16: 120.
10. Cunningham, J. K., Eubank, R. L., Hsing, T., M-type smoothing splines with auxiliary scale estimation, Comput. Statist & Data Anal., 1991, 11: 43.
11. Fan, J., Hu, T., Truong, Y., Robust non-parametric function estimation, Scand. J. Statist., 1994, 21: 433.
12. Welsh, A. H., Robust estimation of smooth regression and spread functions and their derivatives, Statist. Sinica, 1996, 6: 347.
13. Fan, J., Gijbels, I., Data-driven bandwidth selection in local polynomical fitting: variable bandwidth and spatial adaption. J. R. Statist., Soc. B, 1995, 57: 371.
14. Bickel, P. J., One-step Huber estimates in linear models, J. Amer. Stat. Assoc., 1975, 70: 428.
15. Breiman, L., Meisel, W., Purcell, E., Variable kernel estimates of multivariate densities, Technometrics, 1977, 19: 135.
16. Müller, H. -G., Stadtmüller, U., Variable bandwidth kernel estimators of regression curves, Ann. Statist., 1987, 15: 182.
17. Hall, P., Hu, T. C., Marron, J. S., Improved variable window estimators of probability densities, Ann. Statist., 1995, 23: 1.
18. Fan, J., Gijbels, I., Variable bandwidth and local linear regression smoothers, Ann. Statist., 1992, 20: 2008.
19. Gasser, T., Müller, H. -G., Kernel estimation of regression functions, in Smoothing Techniques for Curve Estimation, Lecture Notes in Mathematics, New York: Springer-Verlag, 1979, 23-68.