Electronic Journal of Statistics

Large-sample theory for the Bergsma-Dassios sign covariance

Preetam Nandy, Luca Weihs, and Mathias Drton

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 10, Number 2 (2016), 2287-2311.

Dates
Received: February 2016
First available in Project Euclid: 29 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1472498028

Digital Object Identifier
doi:10.1214/16-EJS1166

Mathematical Reviews number (MathSciNet)
MR3541972

Zentralblatt MATH identifier
1346.62094

Subjects
Primary: 62G10: Hypothesis testing 62G20: Asymptotic properties
Secondary: 62G30: Order statistics; empirical distribution functions

Keywords
Test of independence asymptotics U-statistics nonparametric correlation degeneracy Hoeffding’s D

Citation

Nandy, Preetam; Weihs, Luca; Drton, Mathias. Large-sample theory for the Bergsma-Dassios sign covariance. Electron. J. Statist. 10 (2016), no. 2, 2287--2311. doi:10.1214/16-EJS1166. https://projecteuclid.org/euclid.ejs/1472498028


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