Open Access
September, 1991 On the Balanced Incomplete Block Design for Rankings
M. Alvo, P. Cabilio
Ann. Statist. 19(3): 1597-1613 (September, 1991). DOI: 10.1214/aos/1176348264


A total of $nb$ judges rank $t$ objects $k$ at a time according to $n$ replications of a BIBD with $b$ blocks. The Durbin statistic is commonly used in this context and is equivalent to the usual analysis of variance on the rankings. The approach considered here is to introduce the notion of compatibility so as to define distances between incomplete rankings based on metrics on the space of complete rankings. Through this device we define a class of test statistics which includes the Durbin statistic as a special case, and derive their asymptotic distributions. This analysis also yields a new interpretation of the Durbin statistic.


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M. Alvo. P. Cabilio. "On the Balanced Incomplete Block Design for Rankings." Ann. Statist. 19 (3) 1597 - 1613, September, 1991.


Published: September, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0744.62101
MathSciNet: MR1126340
Digital Object Identifier: 10.1214/aos/1176348264

Primary: 62G10
Secondary: 62E20

Keywords: Bahadur efficiency , Balanced incomplete blocks , concordance , Durbin test , rankings , Spearman and Kendall metrics

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 3 • September, 1991
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