Bounds on Spearman’s rho when at least one random variable is discrete

Mhamed Mesfioui, Julien Trufin, Pierre Zuyderhoff

Research output: Journal PublicationArticlepeer-review

2 Citations (Scopus)

Abstract

Spearman’s rho is one of the most popular dependence measures used in practice to describe the association between two random variables. However, in case of at least one random variable being discrete, Spearman’s correlations are often bounded and restricted to a sub-interval of [- 1 , 1]. Hence, small positive values of Spearman’s rho may actually support a strong positive dependence when getting close to its highest attainable value. Similarly, slight negative values of Spearman’s rho can actually mean a strong negative dependence. In this paper, we derive the best-possible upper and lower bounds for Spearman’s rho when at least one random variable is discrete. We illustrate the obtained lower and upper bounds in some situations of practical relevance.

Original languageEnglish
Pages (from-to)321-348
Number of pages28
JournalEuropean Actuarial Journal
Volume12
Issue number1
DOIs
Publication statusPublished - Jun 2022
Externally publishedYes

Keywords

  • Concordance and discordance
  • Discrete variables
  • Lower bounds
  • Spearman’s rho
  • Upper bounds

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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