Efficient computation of the Bergsma–Dassios sign covariance

Luca Weihs (), Mathias Drton () and Dennis Leung ()
Additional contact information
Luca Weihs: University of Washington
Mathias Drton: University of Washington
Dennis Leung: University of Washington

Computational Statistics, 2016, vol. 31, issue 1, No 14, 315-328

Abstract: Abstract In an extension of Kendall’s $$\tau $$ τ , Bergsma and Dassios (Bernoulli 20(2):1006–1028, 2014) introduced a covariance measure $$\tau ^*$$ τ ∗ for two ordinal random variables that vanishes if and only if the two variables are independent. For a sample of size n, a direct computation of $$t^*$$ t ∗ , the empirical version of $$\tau ^*$$ τ ∗ , requires $$O(n^4)$$ O ( n 4 ) operations. We derive an algorithm that computes the statistic using only $$O \left( n^2\log (n)\right) $$ O n 2 log ( n ) operations.

Keywords: Binary tree; Kendall’s tau; Nonparametric correlation; Spearman’s rho; Rank correlation; Test of independence (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s00180-015-0639-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:31:y:2016:i:1:d:10.1007_s00180-015-0639-x

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s00180-015-0639-x

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

More articles in Computational Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().