The Gaussian rank correlation estimator: Robustness properties

Statistics and Computing

Volumn 22, Issue 2, 2012, Pages 471-483

  Boudt, Kris ^a,b   Cornelissen, Jonathan ^a   Croux, Christophe ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b Lessius University College   (Belgium)

Author keywords

Breakdown; Correlation; Efficiency; Robustness; Van der Waerden

Indexed keywords

EID: 81955160889     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-011-9237-0     Document Type: Article

References (27)

1. Alqallaf, F. A., Konis, K. P., Martin, R. D., Zamar, R. H.: Scalable robust covariance and correlation estimates for data mining. In: Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Edmonton (2002).
2. Alqallaf, F., van Aelst, S., Yohai, V., Zamar, R.: Propagation of outliers in multivariate data. Ann. Stat. 37, 311-331 (2009).
3. Atkinson, A. C., Riani, M., Cerioli, A.: Exploring Multivariate Data with the Forward Search. Springer, Berlin (2004).
4. Bernholt, T., Fischer, P.: The complexity of computing the MCD-estimator. Theor. Comput. Sci. 326, 383-398 (2004).
5. Branco, J. A., Croux, C., Filzmoser, P., Oliveira, M. R.: Robust canonical correlations: A comparative study. Comput. Stat. 20, 203-229 (2005).
6. Capéraà, P., Guillem, A. I. G.: Taux de resistance des tests de rang d'indépendance. Can. J. Stat. 25, 113-124 (1997).
7. Christensen, D.: Fast algorithms for the calculation of Kendall's τ. Comput. Stat. 20, 51-62 (2005).
8. Critchley, F., Schyns, M., Haesbroeck, G.: A relaxed approach to combinatorial problems in robustness and diagnostics. Stat. Comput. 20, 99-115 (2010).
9. Croux, C., Dehon, C.: Influence functions of the Spearman and Kendall correlation measures. Stat. Methods Appl. 19, 497-515 (2010).
10. Croux, C., Haesbroeck, G.: Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies. Biometrika 87, 603-618 (2000).
11. Daudin, J. J., Duby, C., Trecourt, P.: Stability of principal component analysis studied by the bootstrap method. Statistics 19, 241-258 (1988).
12. Davies, P., Gather, U.: Breakdown and groups (with discussion). Ann. Stat. 33, 977-1035 (2005).
13. Devlin, S., Gnanadesikan, R., Kettering, J.: Robust estimation and outlier detection with correlation coefficients. Biometrika 62, 531-545 (1975).
14. Dominici, D. E.: The inverse of the cumulative standard normal probability function. Integral Transforms Spec. Funct. 14, 281-292 (2003).
15. Filzmoser, P., Fritz, H., Kalcher, K.: pcaPP: Robust PCA by Projection Pursuit. R package version 1. 9 (2010).
16. Grize, Y.: Robustheitseigenschaften von Korrelations-schätzungen. Ph. D. thesis, ETH Zürich (1978).
17. Hájek, J., Sidak, Z.: Theory of Rank Tests. Academic Press, New York (1967).
18. Hubert, M., Rousseeuw, P., Vanden Branden, K.: ROBPCA: a new approach to robust principal component analysis. Technometrics 47, 64-79 (2005).
19. Iman, R., Conover, W.: A distribution-free approach to inducing rank correlation among input variables. Commun. Stat., Simul. Comput. 11, 311-334 (1982).
20. Kendall, M.: A new measure of rank correlation. Biometrika 30, 81-93 (1938).
21. Khan, J., van Aelst, S., Zamar, R.: Robust linear model selection based on least angle regression. J. Am. Stat. Assoc. 480, 1289-1299 (2007).
22. Maronna, R., Zamar, R.: Robust estimates of location and dispersion of high-dimensional datasets. Technometrics 44, 307-317 (2002).
23. Maronna, R. A., Martin, R. D., Yohai, V. J.: Robust Statistics: Theory and Methods. Wiley, Chichester (2006).
24. Rousseeuw, P., van Driessen, K.: A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212-223 (1999).
25. Rousseeuw, P., Croux, C., Todorov, V., Ruckstuhl, A., Salibian-Barrera, M., Verbeke, T., Maechler, M.: Robustbase: Basic Robust Statistics. R package version 0. 5-0-1 (2009).
26. Spearman, C.: General intelligence objectively determined and measured. Am. J. Psychol. 15, 201-293 (1904).
27. van Aelst, S., Vandervieren, E., Willems, G.: Robust principal component analysis based on pairwise correlation estimators. In: Proceedings of the 19th International Conference on Computational Statistics, Paris, pp. 573-580 (2010).