Stahel-Donoho kernel estimation for fixed design nonparametric regression models

Science in China, Series A: Mathematics

Volumn 49, Issue 12, 2006, Pages 1879-1896

  Lin, Lu ^a   Cui, Xia ^a  

^a SHANDONG UNIVERSITY   (China)

Author keywords

Kernel estimation; Nonparametric regression; Robustness; Statistical depth

Indexed keywords

EID: 33846537863     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11425-006-2038-9     Document Type: Article

References (21)

1. Nadaraya E A. On estimating regression. Theory Probab Appl, 1964, 9: 141-142
2. Watson G S. Smooth regression analysis. Sankhya Ser A, 1964, 26: 359-372
3. Priestley M B, Chao M T. Non-parametric function fitting. J Roy Statist Soc Ser B, 1972, 34: 385-392
4. Gasser Th, Müller H G. Kernel estimation of regression functions. In: Gasser Th, Rosenblatt M, eds. Smoothing Techniques for Curve Estimation, Lecture Notes in Mathematics, Vol 757. Berlin: Springer-Verlag, 1979, 23-68
5. Hart J D. Nonparametric Smoothing and Lack-of Fit Tests. New York: Springer-Verlag Inc, 1997
6. Zuo Y J, Serfling R. General notions of statistical depth function. Ann Statist, 2000a, 28: 461-482
7. Zuo Y J, Serfling R. Structural properties convergence results for contours of sample statistical depth functions. Ann Statist, 2000b, 28: 483-499
8. Rousseeuw P J, Hubert M. Regression depth. JASA, 1999, 94: 389-433
9. Zuo Y J, Cui H J, He X M. On the Stahel-Donoho estimator and depth-weighed means of multivariate data. Ann Statist, 2004, 32: 167-188
10. Stahel W A. Breakdown of covariance estimators. Research Report 31, Fachgruppe für Statistik, ETH, Zürich, 1981
11. Donoho D L. Breakdown properties of multivariate location estimators. Ph. D Qualifying Paper, Cambridge: Harvard Univ Press, 1982
12. Lin L. Robust depth-weighted wavelet for nonparametric regression models. Acta Mathematica Sinica, English Series, 2005, 21: 585-592
13. Lin L, Chen M H. Robust estimating equation based on statistical depth. Statistical Papers, 2006, 47: 263-278
14. Giloni A, Simonoff J. The conditional breakdown properties of least absolute value local polynomial estimators. Nonparametric Statistics, 2005, 17(1): 15-30
15. Tukey J W. Mathematics and picturing data. Proc Intern Congr Math Vancouver, 1975, 2: 523-531
16. Liu R Y. On a notion of data depth based on random simplices. Ann Statist, 1990, 18: 405-414
17. Zuo Y J. Projection based depth functions and associated median. Ann Statist, 2003, 31: 1460-1490
18. Davies P L, Gather U. Breakdown and groups. Ann Statist, 2005, 33: 977-1035
19. Donoho D L, Huber P J. The notion of breakdown point. In: Pickel P J, Doksum K A, Hodges J L, eds. Jr: A Festchrift for Erich L Lehmann, Wadsworth, Belmont, CA, 1983, 157-148
20. Gurland J. An inequality satisfied by the expectation of the reciprocal of a random variable. Amer Statist, 1967, 21(2): 24-25
21. Serfling R. Approximation Theorems of Mathematical Statistics. New York: Wiley, 1980, 91-95