The Gaussian Rank Correlation Estimator: Robustness Properties

Statistics and Computing, Vol. 22, pp. 471-483, 2012

25 Pages Posted: 13 Oct 2010 Last revised: 4 Mar 2012

See all articles by Kris Boudt

Kris Boudt

Ghent University; Vrije Universiteit Brussel; Vrije Universiteit Amsterdam

Jonathan Cornelissen

KU Leuven - Faculty of Business and Economics (FEB)

Christophe Croux

KU Leuven - Faculty of Business and Economics (FEB)

Date Written: October 8, 2010

Abstract

The Gaussian rank correlation equals the usual correlation coefficient computed from the normal scores of the data. Although its influence function is unbounded, it still has attractive robustness properties. In particular, its breakdown point is above 12%. Moreover, the estimator is consistent and asymptotically efficient at the normal distribution. The correlation matrix based on the Gaussian rank correlation is always positive semidefinite, and very easy to compute, also in high dimensions. A simulation study confirms the good efficiency and robustness properties of the proposed estimator with respect to the popular Kendall and Spearman correlation measures. In the empirical application, we show how it can be used for multivariate outlier detection based on robust principal component analysis.

Keywords: Breakdown, Correlation, Efficiency, Robustness, Van der Waerden

JEL Classification: C13, C15

Suggested Citation

Boudt, Kris and Cornelissen, Jonathan and Croux, Christophe, The Gaussian Rank Correlation Estimator: Robustness Properties (October 8, 2010). Statistics and Computing, Vol. 22, pp. 471-483, 2012, Available at SSRN: https://ssrn.com/abstract=1689465 or http://dx.doi.org/10.2139/ssrn.1689465

Kris Boudt

Ghent University ( email )

Sint-Pietersplein 5
Gent, 9000
Belgium

Vrije Universiteit Brussel ( email )

Pleinlaan 2
http://www.vub.ac.be/
Brussels, 1050
Belgium

Vrije Universiteit Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Jonathan Cornelissen (Contact Author)

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

Naamsestraat 69
Leuven, B-3000
Belgium

Christophe Croux

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

Naamsestraat 69
Leuven, B-3000
Belgium

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
162
Abstract Views
1,145
rank
221,973
PlumX Metrics