Influence functions of the Spearman and Kendall correlation measures

Statistical Methods and Applications

Volumn 19, Issue 4, 2010, Pages 497-515

  Croux, Christophe ^a,b   Dehon, Catherine ^c  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b TILBURG UNIVERSITY   (Netherlands)

^c UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Asymptotic variance; Correlation; Gross error sensitivity; Influence function; Kendall correlation; Robustness; Spearman correlation

Indexed keywords

EID: 77958507047     PISSN: 16182510     EISSN: 1613981X     Source Type: Journal    
DOI: 10.1007/s10260-010-0142-z     Document Type: Article

References (28)

1. Alqallaf FA, Konis KP, Martin RD, Zamar RH (2002) 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.
2. Atkinson AC, Riani M, Cerioli A (2004) Exploring multivariate data with the forward search. Springer, New York.
3. Blomqvist N (1950) On a measure of dependance between two random variables. Ann Math Stat 21: 593-600.
4. Bonett DG, Wright TA (2000) Sample size requirements for estimating Pearson, Kendall and Spearman correlation. Psychometrika 65: 23-28.
5. Borkowf C (2002) Computing the nonnull asymptotic variance and the asymptotic relative efficiency of Spearman's rank correlation. Comput Stat Data Anal 39: 271-286.
6. Caperaa P, Garralda Guillem AI (1997) Taux de resistance des tests de rang d'independance. Can J Stat 25: 113-124.
7. Cerioli A (2010) Multivariate outlier detection with high-breakdown estimators. J Am Stat Assoc (to appear).
8. Croux C, Haesbroeck G (1999) Influence function and efficiency of the minimum covariance determinant scatter matrix estimator. J Multivar Anal 71: 161-190.
9. David FN, Mallows CL (1961) The variance of Spearman's rho in normal samples. Biometrika 48: 19-28.
10. Davies PL, Gather U (2005) Breakdown and groups (with discussion). Ann Stat 33: 977-1035.
11. Devlin SJ, Gnanadesikan R, Kettering JR (1975) Robust estimation and outlier detection with correlation coefficients. Biometrika 62: 531-545.
12. Falk M (1998) A note on the comedian for elliptical distributions. J Multivar Anal 67: 306-317.
13. Genton MG, Ma Y (1999) Robustness properties of dispersion estimators. Stat Probab Lett 44: 343-350.
14. Gnanadesikan R, Kettering JR (1972) Robust estimates, residuals, and outlier detection wit multiresponse data. Biometrics 28: 81-124.
15. Grize YL (1978) Robustheitseigenschaften von Korrelations-schätzungen, Unpublished Diplomarbeit, ETH Zürich.
16. Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA (1986) Robust statistics: the approach based on influence functions. Wiley, New York.
17. Kendall MG (1938) A new measure of rank correlation. Biometrika 30: 81-93.
18. Khan JA, van Aelst S, Zamar RH (2007) Robust linear model selection based on least angle regression. J Am Stat Assoc 480: 1289-1299.
19. Maronna R, Martin D, Yohai V (2006) Robust Statistics. Wiley, New York.
20. Maronna RA, Zamar RH (2002) Robust estimates of location and dispersion of high-dimensional datasets. Technometrics 44: 307-317.
21. Moran PAP (1948) Rank correlation and permutation distributions. Biometrika 44: 142-144.
22. Morgenthaler S (2007) A survey of robust statistics. Stat Methods Appl 15: 271-293.
23. Mosteller F (1946) On some useful inefficient statistics. Ann Math Stat 17: 377.
24. Olkin I, Raveh A (2009) Bounds for how much influence an observation can have. Stat Methods Appl 18: 1-11.
25. Rousseeuw PJ, van Driessen K (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41: 212-223.
26. Shevlyakov GL, Vilchevski NO (2002) Robustness in data analysis: criteria and methods. Modern probability and statistics. VSP, Utrecht.
27. Spearman C (1904) General intelligence objectively determined and measured. Am J Psychol 15: 201-293.
28. Wilcox RR (2003) Inferences based on multiple skipped correlations. Comput Stat Data Anal 44: 223-236.