A relaxed approach to combinatorial problems in robustness and diagnostics

Statistics and Computing

Volumn 20, Issue 1, 2010, Pages 99-115

  Critchley, Frank ^a   Schyns, Michaël ^b   Haesbroeck, Gentiane ^b   Fauconnier, Cécile ^b   Lu, Guobing ^c   Atkinson, Richard A ^d   Wang, Dong Qian ^e  

^a OPEN UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF LIÈGE   (Belgium)

^c UNIVERSITY OF BRISTOL   (United Kingdom)

^d UNIVERSITY OF BIRMINGHAM   (United Kingdom)

^e VICTORIA UNIVERSITY OF WELLINGTON   (New Zealand)

Author keywords

Combinatorial optimisation; Concave functions; Diagnostics; Gravitational functions; Nonlinear optimisation; Robustness

Indexed keywords

EID: 73549118350     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-009-9119-x     Document Type: Article

References (21)

1. Atkinson, A. C.: Masking unmasked. Biometrika 73, 533-541 (1986).
2. Bazaraa, M. S., Sherali, H. D., Shetty, C. M.: Nonlinear Programming: Theory and Algorithms, 2nd edn. Wiley, New York (1993).
3. Conn, A. R., Gould, N. I. M., Toint, P. L.: Trust-Region Methods. MPS-SIAM Series on Optimization (2000).
4. Cook, R. D.: Assessment of local influence (with discussion). J. R. Stat. Soc. B 48, 133-169 (1986).
5. Critchley, F., Atkinson, R. A., Lu, G., Biazi, E.: Influence analysis based on the case sensitivity function. J. R. Stat. Soc. B 63, 307-323 (2001).
6. Critchley, F., Schyns, M., Haesbroeck, G., Kinns, D., Atkinson, R. A., Lu, G.: The case sensitivity function approach to diagnostics and robust computation: a relaxation strategy COMPSTAT 2004. In: Antoch, J. (ed.) Proceedings in Computational Statistics, pp. 113-125. Physica-Verlag, Heidelberg (2004).
7. Danninger, G., Bomze, I.: Using copositivity for global optimality criteria in concave quadratic programming. Math. Program. 62, 575-580 (1993).
8. Gilley, O. W., Kelley Pace, R.: On the Harrison and Rubinfeld data. J. Environ. Econ. Manag. 31, 403-405 (1996).
9. Harrison, D., Rubinfeld, D. L.: Hedonic prices and the demand for clean air. J. Environ. Econ. Manag. 5, 81-102 (1978).
10. Hawkins, D. M.: The Feasible Solution algorithm for least trimmed squares regression. Comput. Stat. Data Anal. 17, 185-196 (1993).
11. Hawkins, D. M.: The Feasible Solution algorithm for the minimum covariance determinant estimator. Comput. Stat. Data Anal. 17, 197-210 (1994).
12. Hawkins, D. M., Olive, D. J.: Improved feasible solution algorithms for high breakdown estimators. Comput. Stat. Data Anal. 30, 1-11 (1999).
13. Hawkins, D. M., Olive, D. J.: Inconsistency of resampling algorithms for high-breakdown regression estimators and a new algorithm. J. Am. Stat. Assoc. 97, 136-147 (2002).
14. Horst, R., Tuy, H.: Global Optimization. Deterministic Approaches, 3rd edn. Springer, Berlin (2003).
15. Pardalos, P. M., Rosen, J. B.: Constrained Global Optimization: Algorithms and Applications. Lecture Notes in Computer Science. Springer, New York (1987).
16. Rousseeuw, P. J.: Multivariate estimation with high breakdown point. In: Grossmann, W., Pflug, G., Vincze, I., Wertz, W. (eds.) Mathematical Statistics and Applications, vol. B, pp. 283-297. Reidel, Dordrecht (1985).
17. Rousseeuw, P. J., Leroy, A. M.: Robust Regression and Outlier Detection. Wiley, New York (1987).
18. Rousseeuw, P. J., van Driessen, K.: A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212-223 (1999).
19. Rousseeuw, P. J., van Driessen, K.: Computing LTS regression for large data sets. Data Mining Knowl. Discov. 12, 29-45 (2006).
20. Sartenaer, A.: Some recent developments in nonlinear optimization algorithms. ESAIM Proc. 13, 41-64 (2003).
21. Schyns, M., Haesbroeck, G., Critchley, F.: RelaxMCD, smooth optimisation for the minimum covariance determinant estimator. HEC-preprint (2008).