The Annals of Statistics

Asymptotic Theory for Measures of Concordance with Special Reference to Average Kendall Tau

Mayer Alvo, Paul Cabilio, and Paul D. Feigin

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Abstract

The problem of $n$ rankings is considered and the asymptotic distributions of measures of concordance based on rank correlations are derived under the null model of complete randomness. The Bahadur efficiencies of the measures are computed. A matrix analysis then reveals the asymptotic distribution and superior efficiency of average Kendall tau. Some interpretation of the results is also made.

Article information

Source
Ann. Statist., Volume 10, Number 4 (1982), 1269-1276.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345992

Digital Object Identifier
doi:10.1214/aos/1176345992

Mathematical Reviews number (MathSciNet)
MR673662

Zentralblatt MATH identifier
0523.62047

JSTOR
links.jstor.org

Subjects
Primary: 62G10: Hypothesis testing
Secondary: 62G20: Asymptotic properties 62E15: Exact distribution theory 62E20: Asymptotic distribution theory

Keywords
$n$ rankings average Kendall's tau Kendall's $W$ Friedman's test Bahadur slope weighted sum of Chi squared variables

Citation

Alvo, Mayer; Cabilio, Paul; Feigin, Paul D. Asymptotic Theory for Measures of Concordance with Special Reference to Average Kendall Tau. Ann. Statist. 10 (1982), no. 4, 1269--1276. doi:10.1214/aos/1176345992. https://projecteuclid.org/euclid.aos/1176345992


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