Bootstrapping robust estimates of regression

Annals of Statistics

Volumn 30, Issue 2, 2002, Pages 556-582

  Salibian Barrera, Matias ^a   Zamar, Ruben H ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Breakdown point; Confidence intervals; Regression

Indexed keywords

EID: 0036284286     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1021379865     Document Type: Article

References (29)

1. BEATON, A. E. and TUKEY, J. W. (1974). The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data. Technometrics 16 147-185.
2. BICKEL, P. J. and FREEDMAN, D. A. (1981). Some asymptotic theory for the bootstrap. Ann. Statist. 9 1196-1217.
3. CARROLL, R. J. (1978). On almost sure expansions for M-estimates. Ann. Statist. 6 314-318.
4. CARROLL, R. J. (1979). On estimating variances of robust estimators when the errors are asymmetric. J. Amer. Statist. Assoc. 74 674-679.
5. CARROLL, R. J. and WELSH, A. H. (1988). A note on asymmetry and robustness in linear regression. Amer. Statist. 42 285-287.
6. COLEMAN, J. (1966). Equality of Educational Opportunity. Office of Education, U.S. Department of Health, Washington, DC.
7. DAVISON, A. C. and HINKLEY, D. V. (1997). Bootstrap Methods and Their Application. Cambridge Univ. Press.
8. EFRON, B. (1979). Bootstrap methods: Another look at the jackknife. Ann. Statist. 7 1-26.
9. FREEDMAN, D. A. (1981). Bootstrapping regression models. Ann. Statist. 9 1218-1228.
10. HAMPEL, F. R., RONCHETTI, E. M., ROUSSEEUW, P. J. and STAHEL, W. A. (1986). Robust Statistics. The Approach Based on Influence Functions. Wiley, New York.
11. HU, F. and KALBFLEISCH, J. D. (2000). The estimating function bootstrap. Canad. J. Statist. 28 449-499.
12. HU, F. and ZIDEK, J. V. (1995). A bootstrap based on the estimating equations of the linear model. Biometrika 82 263-275.
13. HUBER, P. J. (1981). Robust Statistics. Wiley, New York.
14. LIU, R. Y. and SINGH, K. (1992). Efficiency and robustness in resampling. Ann. Statist. 20 370-384.
15. MOSTELLER, F. and TUKEY, J. W. (1977). Data Analysis and Regression. Addison-Wesley, Reading, MA.
16. PARR, W. C. (1985). The bootstrap: Some large sample theory and connections with robustness. Statist. Probab. Lett. 3 97-100.
17. ROCKE, D. M. and DOWNS, G. W. (1981). Estimating the variances of robust estimators of location: Influence curve, jackknife and bootstrap. Comm. Statist. Simulation Comput. 10 221-248.
18. ROUSSEEUW, P. J. and LEROY, A. M. (1987). Robust Regression and Outlier Detection. Wiley, New York.
19. ROUSSEEUW, P. J. and YOHAI, V. J. (1984). Robust regression by means of S-estimators. Robust and Nonlinear Time Series Analysis. Lecture Notes in Statist. 26 256-272. Springer, Berlin.
20. SALIBTAN-BARRERA, M. (2000). Contributions to the theory of robust inference. Ph.D. thesis, Dept. Statist., Univ. British Columbia, Vancouver.
21. SCHUCANY, W. R. and WANG, S. (1991). One-step bootstrapping for smooth iterative procedures. J. Roy. Statist. Soc. Ser. B 53 587-596.
22. SEBER, G. A. F. (1984). Multivariate Observations. Wiley, New York.
23. SERFLING, R. J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.
24. SHAO, J. (1990). Bootstrap estimation of the asymptotic variances of statistical functionals. Ann. Inst. Statist. Math. 42 737-752.
25. SHAO, J. (1992). Bootstrap variance estimators with truncation. Statist. Probab. Lett. 15 95-101.
26. SHORACK, G. R. (1982). Bootstrapping robust regression. Comm. Statist. Theory Methods 11 961-972.
27. SINGH, K. (1998). Breakdown theory for bootstrap quantiles. Ann. Statist. 26 1719-1732.
28. YANG, S.-S. (1985). On bootstrapping a class of differentiable statistical functionals with applications to L- and M-estimates. Statist. Neerlandica 39 375-385.
29. YOHAI, V. J. (1987). High breakdown-point and high efficiency robust estimates for regression. Ann. Statist. 15 642-656.