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2016 Large-sample theory for the Bergsma-Dassios sign covariance
Preetam Nandy, Luca Weihs, Mathias Drton
Electron. J. Statist. 10(2): 2287-2311 (2016). DOI: 10.1214/16-EJS1166

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 $\tau^{*}$ 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.

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Preetam Nandy. Luca Weihs. Mathias Drton. "Large-sample theory for the Bergsma-Dassios sign covariance." Electron. J. Statist. 10 (2) 2287 - 2311, 2016. https://doi.org/10.1214/16-EJS1166

Information

Received: 1 February 2016; Published: 2016
First available in Project Euclid: 29 August 2016

zbMATH: 1346.62094
MathSciNet: MR3541972
Digital Object Identifier: 10.1214/16-EJS1166

Subjects:
Primary: 62G10 , 62G20
Secondary: 62G30

Keywords: asymptotics , Degeneracy , Hoeffding’s D , nonparametric correlation , test of independence , U-statistics

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.10 • No. 2 • 2016
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