Analytical proofs of classical inequalities between Spearman's ρ and Kendall's τ

Christian Genest; Johanna Nešlehová

doi:10.1016/j.jspi.2009.05.017

Analytical proofs of classical inequalities between Spearman's ρ and Kendall's τ

Christian Genest
, Johanna Nešlehová^*

^*Corresponding author for this work

Publication: Scientific journal › Journal article › peer-review

Abstract

Short analytical proofs are given for classical inequalities due to Daniels [1950. Rank correlation and population models. J. Roy. Statist. Soc. Ser. B 12, 171-181; 1951. Note on Durbin and Stuart's formula for E (r_s). J. Roy. Statist. Soc. Ser. B 13, 310] and Durbin and Stuart [1951. Inversions and rank correlation coefficients. J. Roy. Statist. Soc. Ser. B 13, 303-309] relating Spearman's ρ and Kendall's τ.

Original language	English
Pages (from-to)	3795-3798
Number of pages	4
Journal	Journal of Statistical Planning and Inference
Volume	139
Issue number	11
DOIs	https://doi.org/10.1016/j.jspi.2009.05.017
Publication status	Published - 1 Nov 2009
Externally published	Yes

Keywords

Bounds
Jensen's inequality
Kendall's τ
Spearman's ρ

Access to Document

10.1016/j.jspi.2009.05.017

Cite this

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title = "Analytical proofs of classical inequalities between Spearman's ρ and Kendall's τ",

abstract = "Short analytical proofs are given for classical inequalities due to Daniels [1950. Rank correlation and population models. J. Roy. Statist. Soc. Ser. B 12, 171-181; 1951. Note on Durbin and Stuart's formula for E (rs). J. Roy. Statist. Soc. Ser. B 13, 310] and Durbin and Stuart [1951. Inversions and rank correlation coefficients. J. Roy. Statist. Soc. Ser. B 13, 303-309] relating Spearman's ρ and Kendall's τ.",

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N2 - Short analytical proofs are given for classical inequalities due to Daniels [1950. Rank correlation and population models. J. Roy. Statist. Soc. Ser. B 12, 171-181; 1951. Note on Durbin and Stuart's formula for E (rs). J. Roy. Statist. Soc. Ser. B 13, 310] and Durbin and Stuart [1951. Inversions and rank correlation coefficients. J. Roy. Statist. Soc. Ser. B 13, 303-309] relating Spearman's ρ and Kendall's τ.

AB - Short analytical proofs are given for classical inequalities due to Daniels [1950. Rank correlation and population models. J. Roy. Statist. Soc. Ser. B 12, 171-181; 1951. Note on Durbin and Stuart's formula for E (rs). J. Roy. Statist. Soc. Ser. B 13, 310] and Durbin and Stuart [1951. Inversions and rank correlation coefficients. J. Roy. Statist. Soc. Ser. B 13, 303-309] relating Spearman's ρ and Kendall's τ.

KW - Bounds

KW - Jensen's inequality

KW - Kendall's τ

KW - Spearman's ρ

U2 - 10.1016/j.jspi.2009.05.017

DO - 10.1016/j.jspi.2009.05.017

M3 - Journal article

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