On the efficient computation of robust regression estimators

Computational Statistics and Data Analysis

Volumn 54, Issue 12, 2010, Pages 3044-3056

  Flores, Salvador ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

Clustering; Global optimization; Robust regression; Stopping conditions

Indexed keywords

ADAPTIVE ALGORITHMS; GLOBAL OPTIMIZATION; OPTIMIZATION; REGRESSION ANALYSIS;

ALGORITHM PARAMETERS; CLUSTERING; CLUSTERING TECHNIQUES; EFFICIENT COMPUTATION; GLOBAL OPTIMIZATION METHOD; ROBUST REGRESSIONS; STOPPING CONDITIONS;

CLUSTERING ALGORITHMS;

EID: 77955361844     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2010.03.020     Document Type: Article

References (20)

1. Aggarwal, C.H., Hinneburg, A., Keim, D., 2001. On the surprising behaviour of distance metrics in high dimensional space. In: Van den Bussche, J., Vianu, V. (Eds.), ICDT 2001. In: LNCS, vol. 1973. Springer-Verlag, Berlin, Heidelberg, pp. 420-434.
2. Agulló, J., 2001. New algorithms for computing the least trimmed squares regression estimator. Computational Statistics & Data Analysis 36 (4), 425-439. (Pubitemid 32589427)
3. Archetti, F., Schoen, F., 1984. A survey on the global optimization problem: general theory and computational approaches. Annals of Operations Research 1 (2), 87-110.
4. Beyer, K., Goldstein, J., Ramakrishnan, R., Shaft, U., 1998. When is the nearest neighbor meaningful? In: Beeri, C., Buneman, P. (Eds.), ICDT 1999. In: LNCS, vol. 1540. Springer-Verlag, Berlin, Heidelberg, pp. 217-235.
5. Björck, A, 1996. Numerical Methods for Least Squares Problems. SIAM, Philadelphia.
6. Boender, E., Rinnooy Kan, A.H., 1983. A Bayesian analysis of the number of cells of a multinomial distribution. The Statistician 32 (1-2), 240-248.
7. Donoho, D.L., Huber, P., 1983. The notion of breakdown point. In: Bickel, P.J., Doksum, K.A., Hodges, J.L. (Eds.), A Festschrift for Erich L. Lehmann. In: Wadsworth Statist./Probab. Ser., Wadsworth, CA, pp. 157-184.
8. Huber, P., 1981. Robust Statistics. Wiley, New York.
9. Kaufman, L., Rousseeuw, P., 1990. Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.
10. Maronna, R.A., Martin, R.D., Yohai, V.J., 2006. Robust Statistics. Theory and Methods. In: Wiley Series in Probability and Statistics.
11. Nocedal, J., Wright, S., 1999. Numerical Optimization. Springer-Verlag, New York.
12. Piccioni, M., Ramponi, A., 1990. Stopping rules for the multistart method when different local minima have different function values. Optimization 21 (5), 697-707.
13. Rinnooy Kan, A.H., Timmer, G.T., 1987. Stochastic global optimization methods: part I: clustering methods. Mathematical Programming 39 (1), 27-56. (Pubitemid 18550735)
14. Rousseeuw, P., 1984. Least median of squares regression. Journal of the American Statistical Association 79 (388), 871-880.
15. Rousseeuw, P., Van Driessen, K., 2000. An algorithm for positive-breakdown regression based on concentration steps. In: Gaul, W., Opitz, O., Schader, M. (Eds.), Data Analysis: Modeling and Practical Applications. Springer, New York, pp. 335-346.
16. Ruppert, D., 1992. Computing S-estimators for regression and multivariate location/dispersion. Journal of Computational and Graphical Statistics 1 (3), 253-270.
17. Salibian-Barrera, M., Willems, G., Zamar, R.H., 2008. The Fast-τ estimator for regression. Journal of Computational & Graphical Statistics 17 (3), 659-682.
18. Salibian-Barrera, M., Yohai, V., 2006. A fast algorithm for S-regression estimates. Journal of Computational & Graphical Statistics 15 (2), 414-427.
19. Törn, A., .ilinskas, A., 1989. Global Optimization. In: Lecture Notes in Comput. Sci., vol. 350. Springer-Verlag, New York.
20. Yohai, V., Zamar, R.H., 1988. High breakdown-point estimates of regression by means of the minimization of an efficient scale. Journal of the American Statistical Association 83 (402), 406-413.