Spatial sign correlation
Daniel Vogel (University of Aberdeen, UK)
A robust correlation estimator based on the spatial sign covariance matrix (SSCM) is proposed.
We derive its asymptotic distribution and influence function at elliptical distributions. Finite
sample and robustness properties are studied and compared to other robust correlation estimators
by means of numerical simulations. The proposed correlation estimator has a variety of nice
properties. It is fast to compute, distribution-free within the elliptical model, as efficient as
similarly robust estimators, and its asymptotic variance admits an explicit form, which facilitates
Its main drawback is the inefficiency under strongly shaped models, i.e., where the eigenvalues of
the shape matrix strongly differ. The efficiency may be largely improved by a prior componentwise
standardization. We also establish the asymptotic normality of the thus obtained two-step
estimator, and show in particular that the loss due to having to estimate the marginal scales - as
compared known scale - is nil asymptotically. An important consequence is that the asymptotic
variance of the two-step estimator only depends on the correlation coefficient itself. This allows
to devise a variance-stabilizing transformation in the same vein as Fishers z-transformation, but
which is valid for all elliptical distributions.
The talk is based on joint work with Alexander Duerre, Roland Fried and David Tyler.