An easy way to increase the finite-sample efficiency of the resampled minimum volume ellipsoid estimator

Computational Statistics and Data Analysis

Volumn 25, Issue 2, 1997, Pages 125-141

  Croux, Christophe ^a   Haesbroeck, Gentiane ^b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Breakdown point; Finite sample efficiency; Location estimation; Minimum volume ellipsoid; Robustness; Scatter matrix

Indexed keywords

ALGORITHMS; REGRESSION ANALYSIS; ROBUSTNESS (CONTROL SYSTEMS); STATISTICAL METHODS;

BREAKDOWN POINT; FINITE SAMPLE EFFICIENCY; LOCATION ESTIMATION; MINIMUM VOLUME ELLIPSOID ESTIMATOR; SCATTER MATRIX;

ESTIMATION;

EID: 0031193060     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(96)00088-6     Document Type: Article

References (25)

1. Beirlant, J., D.M. Mason and C. Vynckier, Goodness-of-fit tests for multivariate normality based on generalised quantiles, Internal Report (K.U. Leuven, 1996).
2. Cook, R.D., D.M. Hawkins and S. Weisberg, Exact iterative computation of the robust multivariate minimum volume ellipsoid estimator, Statist. and Probab. Lett., 16 (1993) 213-218.
3. Croux C. and P.J. Rousseeuw, A Class of high-breakdown scale estimators based on subranges, Comm. Statist. Theory Methods, Vol. 21 (1992) 1935-1951.
4. Croux, C., P.J. Rousseeuw and A. Van Bael, Robust regression by minimizing nested scale estimators, J. Statist. Plann. Inference, 53 (1996) 197-235.
5. Davies, P.L., Asymptotic behavior of S-estimates of multivariate location parameters and dispersion matrices, Ann. Statist., 15 (1987) 1269-1292.
6. Davies, P.L., The asymptotics of Rousseeuw's minimum volume ellipsoid estimator, Ann. Statist., 20 (1992) 1828-1843.
7. Donoho, D.L. and P.J. Huber, The notion of breakdown point, in: P.J. Bickel, K.A. Doksum and J.L. Hodges, Jr. (Eds.), A Festschrift for Erich L. Lehmann (Wadsworth, California, 1983) 157-184.
8. Einmahl, J.H.J. and D.M. Mason, Generalized quantile processes, Ann. Statist., 20 (1992) 1062-1078.
9. Hampel, F.R., E.M. Ronchetti, P.J. Rousseeuw and W.A. Stahel, Robust statistics: the approach based on influence functions (Wiley, New York, 1986).
10. Hawkins, D.M., A feasible solution algorithm for the minimum volume ellipsoid estimator in multivariate data, Comput. Statist., 8 (1993) 95-107.
11. Hawkins, D.M., A feasible solution algorithm for the minimum covariance determinant estimator, Comput. Statist. Data Anal., 17 (1994) 197-210.
12. Hawkins, D.M. and J.S. Simonoff, AS 282: high breakdown regression and multivariate estimation, Appl. Statist., 42 (1993) 423-432.
13. Hössjer, O., Exact computation of the least-trimmed-squares estimate in simple linear regression, Comput. Statist. Data Anal., 19 (1995) 265-268.
14. Lopuhaä, H.P., Multivariate τ-estimators for location and scatter, Canad. J. Statist., 19 (1991) 307-321.
15. Lopuhaä, H.P. and P.J. Rousseeuw, Breakdown points of affine equivariant estimators of multivariate location and covariance matrices, Ann. Statist., 19 (1991) 229-248.
16. Maronna, R.A. and V.J. Yohai, The behavior of the Stahel-Donoho robust multivariate estimator, J. Amer. Statist. Assoc., 90 (1995) 330-341.
17. Maronna, R.A., W.A. Stahel and V.J. Yohai, Bias-robust estimators of multivariate scatter based on projections, J. Multivariate Anal., 42 (1992) 141-161.
18. Rousseeuw, P.J., Multivariate estimation with high breakdown point, in: W. Grossmann, G. Pflug, I. Vincze and W. Wertz (Eds.), Mathematical statistics and applications, Vol. B (Reidel, Dordrecht, 1985) 283-297.
19. Rousseeuw, P.J. and G.W. Bassett, Robustness of the p-subset algorithm for regression with high breakdown point, in: W. Stahel and S. Weisberg (Eds.), Directions in robust statistics and diagnostics, Part II (Springer, New York, 1991) 185-194.
20. Rousseeuw, P.J. and A.M. Leroy, Robust regression and outlier detection (Wiley, New York, 1987).
21. Rousseeuw, P.J. and B.C. van Zomeren, Unmasking multivariate outliers and leverage points, J. Amer. Statist. Assoc., 85 (1990) 633-639.
22. Ruppert, D., Computing S-estimators for regression and multivariate location/dispersion, J. Comput. Graph. Statist., 1 (1992) 253-270.
23. Tyler, D.E., A distribution-free M-estimator of multivariate scatter, Ann. Statist., 15 (1987) 234-251.
24. Woodruff, D.L. and D.M. Rocke, Heuristic search algorithms for the minimum volume ellipsoid, J. Comput. Graph. Statist., 2 (1993) 69-95.
25. Woodruff, D.L. and D.M. Rocke, Computable robust estimation of multivariate location and shape in high dimension using compound estimators, J. Amer. Statist. Assoc., 89 (1994) 888-896.