  The spatial sign correlation (D\"urre, 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. D\"urre 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.
