A fast algorithm for the minimum covariance determinant estimator

Technometrics

Volumn 41, Issue 3, 1999, Pages 212-223

  Rousseeuw, Peter J ^a   Van Driessen, Katrien ^b  

^a UNIVERSITY OF ANTWERP   (Belgium)

^b Universitaire Faculteiten   (Belgium)

Author keywords

Breakdown value; Multivariate location and scatter; Outlier detection; Regression; Robust estimation

Indexed keywords

DATA REDUCTION; DATA STRUCTURES; GEOMETRY; HEURISTIC METHODS; ITERATIVE METHODS; MATRIX ALGEBRA; PARAMETER ESTIMATION; REGRESSION ANALYSIS; SIMULATED ANNEALING;

BREAKDOWN VALUE; COVARIANCE MATRIX; MINIMUM COVARIANCE DETERMINANT METHOD; MULTIVARIATE LOCATION AND SCATTERER; OUTLIER DETECTION;

ALGORITHMS;

EID: 0032680362     PISSN: 00401706     EISSN: 15372723     Source Type: Journal    
DOI: 10.1080/00401706.1999.10485670     Document Type: Article

References (27)

1. Agullo, J. (1996), “Exact Iterative Computation of the Multivariate Minimum Volume Ellipsoid Estimator With a Branch and Bound Algorithm,” in Proceedings in Computational Statistics, ed. A. Prat, Heidelberg: Physica-Verlag, pp. 175-180.
2. Andrews, D. F., and Herzberg, A. M. (1985), Data, Springer-Verlag, New York.
3. Butler, R. W., Davies, P. L., and Jhun, M. (1993), “Asymptotics for the Minimum Covariance Determinant Estimator,” The Annals of Statistics, 21, 1385-1400.
4. Coakley, C. W., and Hettmansperger, T. P. (1993), “A Bounded Influence, High Breakdown, Efficient Regression Estimator,” Journal of the American Statistical Association, 88, 872-880.
5. Cook, R. D., Hawkins, D. M., and Weisberg, S. (1992), “Exact Iterative Computation of the Robust Multivariate Minimum Volume Ellipsoid Estimator,” Statistics and Probability Letters, 16, 213-218.
6. Croux, C., and Haesbroeck, G. (in press), “Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator,” Journal of Multivariate Analysis.
7. Davies, L. (1992), “The Asymptotics of Rousseeuw’s Minimum Volume Ellipsoid Estimator,” The Annals of Statistics, 20, 1828-1843.
8. Donoho, D. L. (1982), “Breakdown Properties of Multivariate Location Estimators,” unpublished Ph.D. qualifying paper, Harvard University, Dept, of Statistics.
9. Griibel, R. (1988), “A Minimal Characterization of the Covariance Matrix,” Metrika, 35, 49-52.
10. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., and Stahel, W. A. (1986), Robust Statistics, The Approach Based on Influence Functions, New York: Wiley.
11. Hawkins, D. M. (1994), “The Feasible Solution Algorithm for the Minimum Covariance Determinant Estimator in Multivariate Data,” Computational Statistics and Data Analysis, 17, 197-210.
12. Hawkins, D. M., and McLachlan, G. J. (1997). “High-Breakdown Linear Discriminant Analysis,” Journal of the American Statistical Association, 92, 136-143.
13. Hawkins, D. M., and Olive, D. J. (1999), “Improved Feasible Solution Algorithms for High Breakdown Estimation,” Computational Statistics and Data Analysis, 30, 1-11.
14. Lopuhaa, H. P., and Rousseeuw, P. J. (1991), “Breakdown Points of Affine Equivariant Estimators of Multivariate Location and Covariance Matrices,” The Annals of Statistics, 19, 229-248.
15. Maronna, R. A. (1976), “Robust M-estimators of Multivariate Location and Scatter,” The Annals of Statistics, 4, 51-56.
16. Meer, P., Mintz, D., Rosenfeld, A., and Kim, D. (1991), “Robust Regression Methods in Computer Vision: A Review,” International Journal of Computer Vision, 6, 59-70.
17. Nickelson, T. E. (1986), “Influence of Upwelling, Ocean Temperature, and Smolt Abundance on Marine Survival of Coho Salmon (Oncorhynchus Kisutch) in the Oregon Production Area,” Canadian Journal of Fisheries and Aquatic Sciences, 43, 527-535.
18. Odewahn, S. C., Djorgovski, S. G., Brunner, R. J., and Gal, R. (1998), “Data From the Digitized Palomar Sky Survey,” technical report, California Institute of Technology.
19. Rocke, D. M., and Woodruff, D. L. (1996), “Identification of Outliers in Multivariate Data,” Journal of the American Statistical Association, 91, 1047-1061.
20. Rousseeuw, P. J. (1984), “Least Median of Squares Regression,” Journal of the American Statistical Association, 19, 871-880.
21. Rousseeuw, P. J. (1985), “Multivariate Estimation With High Breakdown Point,” in Mathematical Statistics and Applications, Vol B, eds. W. Grossmann, G. Pflug, I. Vincze, and W. Wertz, Dordrecht: Reidel, pp. 283-297.
22. Rousseeuw, P. J. (1997), “Introduction to Positive-Breakdown Methods,” in Handbook of Statistics, Vol. 15: Robust Inference, eds. G. S. Maddala and C. R. Rao, Amsterdam: Elsevier, pp. 101-121.
23. Rousseeuw, P. J., and Leroy, A. M. (1987), Robust Regression and Outlier Detection, New York: Wiley.
24. Rousseeuw, P. J., and van Zomeren, B. C. (1990), “Unmasking Multivariate Outliers and Leverage Points,” Journal of the American Statistical Association, 85, 633-639.
25. Simpson, D. G., Ruppert, D., and Carroll, R. J. (1992), “On One-Step GM-estimates and Stability of Inferences in Linear Regression,” Journal of the American Statistical Association, 87, 439-450.
26. Woodruff, D. L., and Rocke, D. M. (1993), “Heuristic Search Algorithms for the Minimum Volume Ellipsoid,” Journal of Computational and Graphical Statistics, 2, 69-95.
27. Woodruff, D. L., and Rocke, D. M. (1994), “Computable Robust Estimation of Multivariate Location and Shape in High Dimension Using Compound Estimators,” Journal of the American Statistical Association, 89, 888-896.