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

Austrian Journal of Statistics

article

Alexander Dürre¹  Roland Fried¹  Daniel Vogel² 

[1] TU Dortmund;University of Aberdeen

关键词: elliptical distribution;    influence function;    eigenvalues;    fixed-point algorithm.;   

DOI  :  10.17713/ajs.v46i3-4.667

学科分类：医学（综合）

来源: Austrian Statistical Society

【 摘 要 】

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.

【 授权许可】

CC BY