Characterizations of degree one bivariate measures of concordance

    Authors

    H. H. Edwards;M. D. Taylor

    Comments

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    Abbreviated Journal Title

    J. Multivar. Anal.

    Keywords

    Copula; Measure of association; Measure of concordance; Statistics & Probability

    Abstract

    We call a measure of concordance kappa of an ordered pair. (X, Y) of two continuous random variables a bivariate measure of concordance. This kappa may be considered to be a function kappa(C) of the copula C associated with. (X, Y). kappa is considered to be of degree n if, given any two copulas A and B, the value of their convex sum, kappa(tA + (1-t)B), is a polynomial in t of degree n. Examples of bivariate measures of concordance are Spearman's rho, Blomqvist's beta, Gini's measure of association, and Kendall's tau. The first three of these are of degree one, but Kendall's tau is of degree two. We exhibit three characterizations of bivariate measures of concordance of degree one. (C) 2009 Elsevier Inc. All rights reserved.

    Journal Title

    Journal of Multivariate Analysis

    Volume

    100

    Issue/Number

    8

    Publication Date

    1-1-2009

    Document Type

    Article

    Language

    English

    First Page

    1777

    Last Page

    1791

    WOS Identifier

    WOS:000266565200016

    ISSN

    0047-259X

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