Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator

Journal of Multivariate Analysis

Volumn 71, Issue 2, 1999, Pages 161-190

  Croux, Christophe ^a   Haesbroeck, Gentiane ^b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Influence function; minimum covariance determinant estimator; robust estimation; scatter matrix

Indexed keywords

EID: 0001399709     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1999.1839     Document Type: Article

References (26)

1. Bickel P. J., Lehmann E. L. Descriptive statistics for nonparametric models III, Dispersion. Ann. Statist. 4:1976;1139-1159.
2. Butler R. W. Nonparametric interval and point prediction using data trimmed by a Grubbs type outlier rule. Ann. Statist. 10:1982;197-204.
3. Butler R. W., Davies P. L., Jhun M. Asymptotics for the minimum covariance determinant estimator. Ann. Statist. 21:1993;1385-1400.
4. Croux C., Rousseeuw P. J. A class of high-breakdown scale estimators based on subranges. Comm. Statist. Theory Methods. 21:1992;1935-1951.
5. Croux C., Haesbroeck G. Technical Report. 1999.
6. Davies P. L. Asymptotic behavior of S-estimators of multivariate location parameters and dispersion matrices. Ann. Statist. 15:1987;1269-1292.
7. Davies P. L. The asymptotics of Rousseeuw's minimum volume ellipsoid. Ann. Statist. 20:1992a;1828-1843.
8. Davies P. L. An efficient Fréchet Differentiable high breakdown multivariate location and dispersion estimator. J. Multivariate Anal. 40:1992b;311-327.
9. Grübel R. A minimal characterization of the covariance matrix. Metrika. 35:1988;49-52.
10. Hampel F. R., Ronchetti E. M., Rousseeuw P. J., Stahel W. A. Robust Statistics: The Approach Based on Influence Functions. 1996;Wiley, New York.
11. Hawkins D. M. The feasible solution algorithm for the minimum covariance determinant estimator in multivariate data. Comput. Statist. Data Anal. 17:1994;197-210.
12. He X., Wang G. Cross-checking using the minimum volume ellipsoid estimator. Statistica Sinica. 6:1996;367-374.
13. Hössjer O., Croux C. Generalizing univariate signed rank statistics for testing and estimating a multivariate location parameter. Nonparametric Statist. 4:1995;293-308.
14. Lopuhaä H. P. On the relation between S-estimators and M-estimators of multivariate location and covariance. Ann. Statist. 17:1989;1662-1683.
15. Lopuhaä H. P. Multivariate τ-estimators for location and scatter. Canad. J. Statist. 19:1991;307-321.
16. Lopuhaä H. P. Highly efficient estimators of multivariate location with high breakdown point. Ann. Statist. 19:1992;229-248.
17. H. P. Lopuhaä, Asymptotics of reweighted estimators of multivariate location and scatter, preprint, TU Delft, 1997.
18. Lopuhaä H. P., Rousseeuw P. J. Breakdown properties of affine equivariant estimators of multivariate location and covariance matrices. Ann. Statist. 19:1991;229-248.
19. Maronna R. A., Yohai. Robust estimation of multivariate location and scatter. Kotz S., Read C., Banks D. Encyclopedia of Statistical Sciences Update. 1998;589-596 Wiley, New York.
20. Rocke D. M. Robustness properties of S-estimators of multivariate location and shape in high dimensions. Ann. Statist. 24:1996;1327-1345.
21. Rousseeuw P. J. Multivariate estimation with high breakdown point. Grossmann W., Pflug G., Vincze I., Wertz W. Mathematical Statistics and Applications. 1985;283-297 Reidel, Dordrecht.
22. Rousseeuw P. J., Leroy A. M. Robust Regression and Outlier Detection. 1987;Wiley, New York.
23. Rousseeuw P. J., Croux C. The bias of k-step M-estimators. Statist. Probab. Lett. 20:1994;411-420.
24. P. J. Rousseeuw, and, K. Van Driessen, A fast algorithm for the minimum covariance determinant estimator, Technometrics, to appear.
25. Ruppert D. Computing S-estimators for regression and multivariate location/dispersion. J. Comput. Graph. Statist. 1:1992;253-270.
26. Yohai V. J., Maronna R. A. The maximum bias of robust covariances. Comm. Statist. A. 19:1990;3924-3933.