High-breakdown estimators of multivariate location and scatter

Robustness and Complex Data Structures: Festschrift in Honour of Ursula Gather

Volumn , Issue , 2013, Pages 49-66

  Rousseeuw, Peter ^a   Hubert, Mia ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR TRANSFORMATIONS; MATHEMATICAL TRANSFORMATIONS; STATISTICS;

ELLIPTICAL DISTRIBUTIONS; HIGH BREAKDOWN ESTIMATORS; LOCATION VECTOR; MINIMUM COVARIANCE DETERMINANT; POSITIVE DEFINITE; ROBUST ESTIMATORS; ROBUST METHODS; SCATTER MATRIX;

LOCATION;

EID: 84908157998     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-642-35494-6_4     Document Type: Chapter

References (35)

1. Becker, C., & Gather, U. (1999). The masking breakdown point of multivariate outlier identification rules. Journal of the American Statistical Association, 94, 947-955.
2. Becker, C., & Gather, U. (2001). The largest nonidentifiable outlier: a comparison of multivariate simultaneous outlier identification rules. Computational Statistics & Data Analysis, 36, 119-127.
3. Billor, N., Hadi, A., & Velleman, P. (2000). BACON: blocked adaptive computationally efficient outlier nominators. Computational Statistics & Data Analysis, 34, 279-298.
4. Cator, E., & Lopuhaä, H. (2012). Central limit theorem and influence function for the MCD estimators at general multivariate distributions. Bernoulli, 18, 520-551.
5. Croux, C., & Haesbroeck, G. (1999). Influence function and efficiency of theMinimum Covariance Determinant scatter matrix estimator. Journal of Multivariate Analysis, 71, 161-190.
6. Davies, L. (1987). Asymptotic behavior of S-estimators of multivariate location parameters and dispersion matrices. The Annals of Statistics, 15, 1269-1292.
7. Davies, P., & Gather, U. (2005). Breakdown and groups (with discussion and rejoinder). The Annals of Statistics, 33, 977-1035.
8. Debruyne, M., & Hubert, M. (2009). The influence function of the Stahel-Donoho covariance estimator of smallest outlyingness. Statistics & Probability Letters, 79, 275-282.
9. Donoho, D. (1982). Breakdown properties of multivariate location estimators. Ph.D. Thesis, Harvard University, Boston.
10. Fritz, H., Filzmoser, P., & Croux, C. (2012). A comparison of algorithms for the multivariate L1-median. Computational Statistics, 27, 393-410.
11. Gather, U., & Hilker, T. (1997). A note on Tyler's modification of the MAD for the Stahel-Donoho estimator. The Annals of Statistics, 25, 2024-2026.
12. Gnanadesikan, R., & Kettenring, J. (1972). Robust estimates, residuals, and outlier detection with multiresponse data. Biometrics, 28, 81-124.
13. Hampel, F., Ronchetti, E., Rousseeuw, P., & Stahel, W. (1986). Robust statistics: the approach based on influence functions. New York: Wiley.
14. Hubert, M., Rousseeuw, P., & Vanden Branden, K. (2005). ROBPCA: a new approach to robust principal components analysis. Technometrics, 47, 64-79.
15. Hubert, M., Rousseeuw, P., & Verdonck, T. (2012). A deterministic algorithm for robust location and scatter. Journal of Computational and Graphical Statistics, 21, 618-637.
16. Lopuhaä, H. (1989). On the relation between S-estimators and M-estimators of multivariate location and covariance. The Annals of Statistics, 17, 1662-1683.
17. Lopuhaä, H., & Rousseeuw, P. (1991). Breakdown points of affine equivariant estimators of multivariate location and covariance matrices. The Annals of Statistics, 19, 229-248.
18. Maronna, R. (1976). RobustM-estimators of multivariate location and scatter. The Annals of Statistics, 4, 51-67.
19. Maronna, R., Martin, D., & Yohai, V. (2006). Robust statistics: theory and methods. New York: Wiley.
20. Maronna, R.,&Yohai, V. (1995). The behavior of the Stahel-Donoho robust multivariate estimator. Journal of the American Statistical Association, 90, 330-341.
21. Maronna, R., & Zamar, R. (2002). Robust estimates of location and dispersion for highdimensional data sets. Technometrics, 44, 307-317.
22. Pison, G., Van Aelst, S., & Willems, G. (2002). Small sample corrections for LTS and MCD. Metrika, 55, 111-123.
23. Rousseeuw, P. (1984). Least median of squares regression. Journal of the American Statistical Association, 79, 871-880.
24. Rousseeuw, P. (1985). Multivariate estimation with high breakdown point. In W. Grossmann, G. Pflug, I. Vincze, & W. Wertz (Eds.), Mathematical statistics and applications (Vol. B, pp. 283-297). Dordrecht: Reidel.
25. Rousseeuw, P., & Croux, C. (1993). Alternatives to the median absolute deviation. Journal of the American Statistical Association, 88, 1273-1283.
26. Rousseeuw, P., & Leroy, A. (1987). Robust regression and outlier detection. New York: Wiley-Interscience.
27. Rousseeuw, P., & Van Driessen, K. (1999). A fast algorithm for the minimum covariance determinant estimator. Technometrics, 41, 212-223.
28. Rousseeuw, P., & van Zomeren, B. (1990). Unmasking multivariate outliers and leverage points. Journal of the American Statistical Association, 85, 633-651.
29. Salibian-Barrera, M., Van Aelst, S., & Willems, G. (2006). PCA based on multivariate MMestimators with fast and robust bootstrap. Journal of the American Statistical Association, 101, 1198-1211.
30. Salibian-Barrera, M., & Yohai, V. J. (2006). A fast algorithm for S-regression estimates. Journal of Computational and Graphical Statistics, 15, 414-427.
31. Stahel, W. (1981). Robuste Schätzungen: infinitesimale Optimalität und Schätzungen von Kovarianzmatrizen. Ph.D. Thesis, ETH Zürich.
32. Tatsuoka, K., & Tyler, D. (2000). On the uniqueness of S-functionals and M-functionals under nonelliptical distributions. The Annals of Statistics, 28, 1219-1243.
33. Verboven, S., & Hubert, M. (2005). LIBRA: a Matlab library for robust analysis. Chemometrics and Intelligent Laboratory Systems, 75, 127-136.
34. Visuri, S., Koivunen, V., & Oja, H. (2000). Sign and rank covariance matrices. Journal of Statistical Planning and Inference, 91, 557-575.
35. Yohai, V., & Zamar, R. (1988). High breakdown point estimates of regression by means of the minimization of an efficient scale. Journal of the American Statistical Association, 83, 406-413.