A new weighted rank coefficient of concordance

There are many situations where n objects are ranked by b>2 independent sources or observers and in which the interest is focused on agreement on the top rankings. Kendall's coefficient of concordance 10 M. Kendall and B. Smith, The problem of m rankings, Ann. Math. Stat. 10 (1939), pp. 275–287. doi: 10.1214/aoms/1177732186Crossref] , Google Scholar]] assigns equal weights to all rankings. In this paper, a new coefficient of concordance is introduced which is more sensitive to agreement on the top rankings. The limiting distribution of the new concordance coefficient under the null hypothesis of no association among the rankings is presented, and a summary of the exact and approximate quantiles for this coefficient is provided. A simulation study is carried out to compare the performance of Kendall's, the top-down and the new concordance coefficients in detecting the agreement on the top rankings. Finally, examples are given for illustration purposes, including a real data set from financial market indices.