Multivariate regression S-estimators for robust estimation and inference

Statistica Sinica

Volumn 15, Issue 4, 2005, Pages 981-1001

  Van Aelst, Stefan ^a   Willems, Gert ^b  

^a GHENT UNIVERSITY   (Belgium)

^b UNIVERSITY OF ANTWERP   (Belgium)

Author keywords

Breakdown point; Influence function; Robust bootstrap

Indexed keywords

EID: 30744437137     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (29)

1. Adrover, J., Salibian-Barrera, M. and Zamar, R. (2004). Globally robust inference for the location and simple regression models. J. Statist. Plann. Inference 119, 353-375.
2. Agulló, J., Croux, C. and Van Aelst, S. (2002). The multivariate least trimmed squares estimator. Submitted.
3. Berrendero, J. R. and Zamar, R. H. (2001). Maximum bias curves for robust regression with non-elliptical regressors. Ann. Statist. 29, 224-251.
4. Bilodeau, M. and Duchesne, P. (2000). Robust estimation of the SUR model. Canad. J. Statist. 28, 277-288.
5. Davies, P. L. (1987). Asymptotic behavior of S-estimates of multivariate location parameters and dispersion matrices. Ann. Statist. 15, 1269-1292.
6. Davison, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and their Application. Cambridge Univ. Press.
7. Daudin, J., Duby, C. and Trecourt, P. (1988). Stability of principal component analysis studied by the bootstrap method. Statistics 19, 241-258.
8. Donoho, D. L. and Huber, P. J. (1983). The notion of breakdown point. In A Festschrift for Erich Lehmann (Edited by P. Bickel, K. Doksum and J. L. Hodges), 157-184. Wadsworth, Belmont, CA.
9. Efron, B. (1979). Bootstrap methods: another look at the jackknife. Ann. Statist. 7, 1-26.
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. Huber, P. J. (1981). Robust Statistics. Wiley, New York
12. Johnson, R. A. and Wichern, D. W. (1988). Applied Multivariate Statistical Analysis. 2nd Edition. Prentice-Hall.
13. Koenker, R. and Portnoy, S. (1990). M estimation of multivariate regressions. J. Amer. Statist. Assoc. 85, 1060-1068.
14. Lopuhaä, H. (1989). On the relation between S-estimators and M-estimators of multivariate location and covariance. Ann. Statist. 17, 1662-1683.
15. Lopuhaä, H. and Rousseeuw, P. J. (1991). Breakdown points of affine equivariant estimators of multivariate location and covariance matrices. Ann. Statist. 19, 229-248.
16. Maronna, R. A. and Yohai, V. J. (1997). Robust estimation in simultaneous equation models. J. Statist. Plann. Inference 57, 233-244.
17. Ollila, E., Hettmansperger, T. P. and Oja, H. (2002). Estimates of regression coefficients based on sign covariance matrix. J. Roy. Statist. Soc. Ser. B 64, 447-466.
18. Ollila, E., Oja, H. and Koivunen, V. (2003). Estimates of regression coefficients based on lift rank covariance matrix. J. Amer. Statist. Assoc. 98, 90-98.
19. Rousseeuw, P. J. and Leroy, A. M. (1987). Robust Regression and Outlier Detection. Wiley, New York.
20. Rousseeuw, P. J., Van Aelst, S., Van Driessen, K. and Agulló, J. (2004). Robust multivariate regression. Technometrics 46, 293-305.
21. 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.
22. Ruppert, D. (1992). Computing S estimators for regression and multivariate location/dispersion. J. Comput. Graph. Statist. 1, 253-270.
23. Salibian-Barrera, M. (2003a). The asymptotics of MM-estimators for linear regression with fixed design. Preprint, available at http://mathstat.carleton. ca/~matias/pubs.html
24. Salibian-Barrera, M. (2003b). Bootstrapping MM-estimators for linear regression with fixed design. Preprint, available at http://mathstat.carleton. ca/~matias/pubs.html
25. Salibian-Barrera, M. and Zamar, R. (2002). Bootstrapping robust estimates of regression. Ann. Statist. 30, 556-582.
26. Singh, K. (1998). Breakdown theory for bootstrap quantiles. Ann. Statist. 26, 1719-1732.
27. Stromberg, A.J. (1997). Robust covariance estimates based on resampling. J. Statist. Plann. Inference 57, 321-334.
28. Tatsuoka, K. S. and Tyler, D. E. (2000). On the uniqueness of S-functionals and M-functionals under nonelliptical distributions. Ann. Statist. 28, 1219-1243.
29. Van Aelst, S. and Willems, G. (2004). Multivariate regression S-estimators for robust estimation and inference. Technical report, available at http://users.ugent.be/~svaelst/publications. html