Spatial sign correlation

Dürre, Alexander; Vogel, Daniel; Fried, Roland

doi:10.1016/j.jmva.2014.12.002

Cited by 17 publications

(29 citation statements)

References 43 publications

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“…For details see Dürre et al (2015). However, spatial signs can also be used to estimate R.X/ under ellipticity and hence to devise tests that specifically concern R.X/.…”

Section: Discussion and Outlookmentioning

confidence: 99%

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Modern Nonparametric, Robust and Multivariate Methods

Nordhausen¹,

Taskinen²

2015

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“…For details see Dürre et al (2015). However, spatial signs can also be used to estimate R.X/ under ellipticity and hence to devise tests that specifically concern R.X/.…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…Affine equivariance is a very handy property. The exact connection between S.X/ and V.X/ (up to proportionality) seems to be known only for p D 2 (Dürre et al 2015). W.X/ / V.X/, cf.…”

Section: The Spatial Sign Covariance Matrixmentioning

confidence: 99%

Modern Nonparametric, Robust and Multivariate Methods

Nordhausen¹,

Taskinen²

2015

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“…This was proposed in Dürre, Vogel, and Fried (2015). Equation (3) allows an alternative approach: First standardize the data marginally by a robust scale estimator and compute the SSCM of the transformed data.…”

Section: The Multivariate Spatial Sign Correlation Matrixmentioning

confidence: 99%

“…For p = 2, Proposition 1 is a special case of Proposition 4 in Dürre et al (2015) which gives the influence function for arbitrary V . Although Proposition 1 is restricted to the situation where there is only contamination in the first two components, it provides evidence that the sensitivity of the multivariate spatial sign correlation increases with increasing dimension.…”

Section: Sensitivity To Outliersmentioning

confidence: 99%

The Spatial Sign Covariance Matrix and Its Application for Robust Correlation Estimation

Dürre

Fried

Vogel

2017

AJS

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We summarize properties of the spatial sign covariance matrix and especially consider the relationship between its eigenvalues and those of the shape matrix of an elliptical distribution. The explicit relationship known in the bivariate case was used to construct the spatial sign correlation coefficient, which is a non-parametric and robust estimator for the correlation coefficient within the elliptical model. We consider a multivariate generalization, which we call the multivariate spatial sign correlation matrix. A small simulation study indicates that the new estimator is very efficient under various elliptical distributions if the dimension is large. We furthermore derive its influence function under certain conditions which indicates that the multivariate spatial sign correlation becomes more sensitive to outliers as the dimension increases.

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confidence: 99%

Asymptotics of the two-stage spatial sign correlation

Dürre

Vogel

2016

Journal of Multivariate Analysis

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The spatial sign correlation (Dürre, Vogel and Fried, 2015) is a highly robust and easy-to-compute, bivariate correlation estimator based on the spatial sign covariance matrix. Since the estimator is inefficient when the marginal scales strongly differ, a two-stage version was proposed. In the first step, the observations are marginally standardized by means of a robust scale estimator, and in the second step, the spatial sign correlation of the thus transformed data set is computed. Dürre et al. (2015) give some evidence that the asymptotic distribution of the two-stage estimator equals that of the spatial sign correlation at equal marginal scales by comparing their influence functions and presenting simulation results, but give no formal proof. In the present paper, we close this gap and establish the asymptotic normality of the two-stage spatial sign correlation and compute its asymptotic variance for elliptical population distributions. We further derive a variance-stabilizing transformation, similar to Fisher's z-transform, and numerically compare the small-sample coverage probabilities of several confidence intervals. We call ρ = v12/ √ v11v22 the generalized correlation coefficient of the bivariate elliptical distribution F . It is defined without any moments assumptions and coincides with the usual product moment correlation if second moments are finite.

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Spatial sign correlation

Cited by 17 publications

References 43 publications

Modern Nonparametric, Robust and Multivariate Methods

Modern Nonparametric, Robust and Multivariate Methods

The Spatial Sign Covariance Matrix and Its Application for Robust Correlation Estimation

Asymptotics of the two-stage spatial sign correlation

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