Efficient Computation of the Bergsma-Dassios Sign Covariance

Luca Weihs; Mathias Drton; Dennis Leung

Efficient Computation of the Bergsma-Dassios Sign Covariance

Computation 2015-12-31 v2

Authors: Luca Weihs , Mathias Drton , Dennis Leung

Abstract

In an extension of Kendall's $\tau$ , Bergsma and Dassios (2014) introduced a covariance measure $\tau^*$ 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 $t^*$ , the empirical version of $\tau^*$ , requires $O(n^4)$ operations. We derive an algorithm that computes the statistic using only $O(n^2\log(n))$ operations.

Keywords

ordinal random variable sign covariance Bergsma-Dassios Kendall's tau independence efficient computation algorithm

Cite

@article{arxiv.1504.00964,
  title  = {Efficient Computation of the Bergsma-Dassios Sign Covariance},
  author = {Luca Weihs and Mathias Drton and Dennis Leung},
  journal= {arXiv preprint arXiv:1504.00964},
  year   = {2015}
}

Comments

Improved formatting, added reference to R package implementing the algorithm, and added additional experiments

Efficient Computation of the Bergsma-Dassios Sign Covariance

Abstract

Keywords

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