Large-Sample Theory for the Bergsma-Dassios Sign Covariance

2016/02/13 by Preetam Nandy, Nandy, Preetam, Luca Weihs +3 · 2 citations
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1602.04387

arxiv created 2016/02/13 · arxiv updated 2016/02/16

Abstract

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 τ^* 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 τ^*. 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.

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