Influence Functions of the Spearman and Kendall Correlation Measures

CentER Discussion Paper Series No. 2010-40

17 Pages Posted: 7 Apr 2010

See all articles by Christophe Croux

Christophe Croux

KU Leuven - Faculty of Business and Economics (FEB)

Catherine Dehon

Université Libre de Bruxelles (ULB); Université Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES); Université Libre de Bruxelles (ULB) - Solvay Brussels School of Economics and Management

Date Written: March 30, 2010

Abstract

Nonparametric correlation estimators as the Kendall and Spearman correlation are widely used in the applied sciences. They are often said to be robust, in the sense of being resistant to outlying observations. In this paper we formally study their robustness by means of their influence functions and gross-error sensitivities. Since robustness of an estimator often comes at the price of an increased variance, we also compute statistical efficiencies at the normal model. We conclude that both the Spearman and Kendall correlation estimators combine a bounded and smooth influence function with a high efficiency. In a simulation experiment we compare these nonparametric estimators with correlations based on a robust covariance matrix estimator.

Keywords: Asymptotic Variance, Correlation, Gross-Error Sensitivity, Influence function, Kendall correlation, Robustness, Spearman correlation

JEL Classification: C13, C14

Suggested Citation

Croux, Christophe and Dehon, Catherine, Influence Functions of the Spearman and Kendall Correlation Measures (March 30, 2010). CentER Discussion Paper Series No. 2010-40, Available at SSRN: https://ssrn.com/abstract=1585216 or http://dx.doi.org/10.2139/ssrn.1585216

Christophe Croux (Contact Author)

KU Leuven - Faculty of Business and Economics (FEB) ( email )

Naamsestraat 69
Leuven, B-3000
Belgium

Catherine Dehon

Université Libre de Bruxelles (ULB) ( email )

CP 132 Av FD Roosevelt 50
Brussels, Brussels 1050
Belgium
0032 26503858 (Phone)

Université Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES) ( email )

Ave. Franklin D Roosevelt, 50 - C.P. 114
Brussels, B-1050
Belgium
0032 26503858 (Phone)

Université Libre de Bruxelles (ULB) - Solvay Brussels School of Economics and Management ( email )

19 Av Franklin Roosevelt
1050
Brussels
Belgium
0032 26503858 (Phone)

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
139
Abstract Views
1,055
Rank
375,126
PlumX Metrics