  The Bergsma-Dassios sign covariance is a recently proposed extension of
Kendall's tau. In contrast to tau or also Spearman's rho, the new sign
covariance $\tau^*$ vanishes if and only if the two considered random variables
are independent. Specifically, this result has been shown for continuous as
well as discrete variables. We develop large-sample distribution theory for the
empirical version of $\tau^*$. In particular, we use theory for degenerate
U-statistics to derive asymptotic null distributions under independence and
demonstrate in simulations that the limiting distributions give useful
approximations.
