Asymptotics of the two-stage spatial sign correlation

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• 作者：Alexander Dü ; rre^a ; ^{alexander.duerre@udo.edu" class="auth_mail" title="E-mail the corresponding author} ; Daniel Vogel^b
• 关键词：62H12 ; 62G05 ; 62G35
• 刊名：Journal of Multivariate Analysis
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：144
• 期：Complete
• 页码：54-67
• 全文大小：435 K

文摘

The spatial sign correlation (Dürre et al., 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 in the same vein a Fisher’s 626&_mathId=si1.gif&_user=111111111&_pii=S0047259X15002626&_rdoc=1&_issn=0047259X&md5=847ff3149baae0dd1f1f8d45ad1b8593" title="Click to view the MathML source">z$z$-transform. This variance-stabilizing transform is valid for all elliptical distributions and yields very accurate confidence intervals.