Influence functions of the Spearman and Kendall correlation measures

By Christophe Croux, Catherine Dehon. Stat. Methods Appl., 2010

629 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7bb21d4d4505db402d70c383962d19c42d9a7cbe

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Citations in the corpus

Robust High-Dimensional Precision Matrix Estimation (2014, methodology): “Quadrant correlation is less efficient than Gaussian rank correlation and Spearman correlation [Croux and Dehon, 2010].”
Comparing the Pearson and Spearman correlation coefficients across distributions and sample sizes: A tutorial using simulations and empirical data. (2016, methodology): “The smaller variability of r p compared to r s is consistent with previous research (Bonett & Wright, 2000; Croux & Dehon, 2010; Fieller et al., 1957) and suggests that when both population variables are known to have approximately normal distributions, r p should be used instead of r s ,…”
Robust Forecasting of Dynamic Conditional Correlation GARCH Models (2013, background): “robustness, as shown by Croux and Dehon (2010). The locality is needed such that S̃ ′ tSC −1 t S̃t is approximately chi-square distributed with N degrees of freedom (see Subsection 3.”
A Modified CRITIC Method to Estimate the Objective Weights of Decision Criteria (2021, methodology): “This correlation test was chosen due to its appropriateness as a non-parametric test that efficiently measures the association between two different ordinal data arrays [58], apart from its computational simplicity [59].”