Consistency and asymptotic distribution of the Theil-Sen estimator

Journal of Statistical Planning and Inference

Volumn 138, Issue 6, 2008, Pages 1836-1850

  Peng, Hanxiang ^a   Wang, Shaoli ^b   Wang, Xueqin ^c,d  

^a UNIVERSITY OF MISSISSIPPI   (United States)

^b YALE UNIVERSITY SCHOOL OF MEDICINE   (United States)

^c SUN YAT SEN UNIVERSITY   (China)

^d YALE UNIVERSITY   (United States)

Author keywords

Asymptotic normality; Linear regression; Median; Robustness; Super efficiency

Indexed keywords

EID: 39449137098     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2007.06.036     Document Type: Article

References (24)

1. Arcones M.A., Chen Z., and Giné E. Estimators related to U-processes with applications to multivariate medians: asymptotic normality. Ann. Statist. 22 (1994) 1460-1477
2. Akritas M.G., Murphy S.A., and LaValley M.P. The Theil-Sen estimator with doubly censored data and applications to astronomy. J. Amer. Statist. Assoc. 90 (1995) 170-177
3. m estimates. Ann. Statist. 26 (1998) 771-777
4. Dietz E.J. A comparison of robust estimators in simple linear regression. Comm. Statist., Part B Simulation Comput. 16 (1987) 1209-1227
5. Ferguson T.S. A Course in Large Sample Theory. first ed. (1996), Chapman & Hall, New York
6. Fernandes R., and Leblanc S.G. Parametric (modified least squares) and non-parametric (Theil-Sen) linear regressions for predicting biophysical parameters in the presence of measurement errors. Remote Sensing of Environment 95 (2005) 303-316
7. Hoeffding W. A class of statistics with asymptotically normal distribution. Ann. Math. Statist. 19 (1948) 293-325
8. Hoeffding W. Probability inequalities for sums of bounded variables. J. Amer. Statist. Assoc. 50 (1963) 13-30
9. Hollander, M., Wolfe, D.A., 1973. Nonparametric Statistical Methods, first ed., Wiley, New York, pp. 205-206.
10. Hollander, M., Wolfe, D.A., 1999. Nonparametric Statistical Methods, second ed., Wiley, New York, pp. 421-423.
11. Jones M.P. A class of semi-parametric regressions for the accelerated failure time model. Biometrika 84 (1997) 73-84
12. Koenker R. Quantile Regression (2005), Cambridge University Press, Cambridge
13. Mount D.M., and Netanyahu N.S. Efficient randomized algorithms for robust estimation of circular arcs and aligned ellipses. Comput. Geometry: Theory Appl. 19 (2001) 1-33
14. Oja H. Descriptive statistics for multivariate distributions. Statist. Probab. Lett. 1 (1983) 327-332
15. Oja, H., Niinimaa, A., 1984. On robust estimation of regression coefficients. Research Report, Department of Applied Mathematics and Statistics, University of Oulu, Finland.
16. Rousseeuw P.J., and Leroy A.M. Robust Regression and Outlier Detection (2003), Wiley, New York
17. Schick A., and Wefelmeyer W. Root n consistent and optimal density estimators for moving average processes. Scandi. J. Statist. 31 (2004) 63-78
18. Sen P.K. Estimates of the regression coefficient based on Kendall's tau. J. Amer. Statist. Assoc. 63 (1968) 1379-1389
19. Sprent P. Applied Nonparametric Statistical Methods. second ed. (1993), CRC Press, New York
20. Smirnov N.V. Limit distributions for the terms of a variational series. Amer. Math. Soc. Transl. 67 (1952) 82-143
21. Theil H. A rank-invariant method of linear and polynomial regression analysis. Nederl. Akad. Wetench. Ser. A 53 (1950) 386-392
22. Wang X.Q. Asymptotics of the Theil-Sen estimator in simple linear regression models with a random covariate. Nonparametric Statist. 17 (2005) 107-120
23. Wilcox R.R. Simulations on the Theil-Sen regression estimator with right-censored data. Statist. Probab. Lett. 39 (1998) 43-47
24. Zhou, W., Serfling, R., 2007. A Bahadur-Kiefer representation for multivariate spatial U-quantiles. Preprint.