The Annals of Statistics

Majorization, Entropy and Paired Comparisons

Harry Joe

Full-text: Open access

Abstract

Constrained majorization orderings and entropy functions are used to study the class of probability matrices associated with paired comparisons. Majorization orderings are also defined to handle the cases of order effects and/or ties. Results are obtained for maximal and minimal probability matrices with respect to the majorization ordering; these are related to transitivity conditions. The Bradley-Terry and Thurstone-Mosteller models are shown to be maximum entropy models. New models based on maximum entropy are obtained for the cases of order effects and ties; these models are compared with the Davidson and Beaver, the Rao and Kupper and the Davidson models. Applications to professional baseball and hockey are given.

Article information

Source
Ann. Statist., Volume 16, Number 2 (1988), 915-925.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350843

Digital Object Identifier
doi:10.1214/aos/1176350843

Mathematical Reviews number (MathSciNet)
MR947585

Zentralblatt MATH identifier
0721.62067

JSTOR
links.jstor.org

Subjects
Primary: 62J15: Paired and multiple comparisons
Secondary: 06A10

Keywords
Majorization entropy paired comparison Bradley-Terry model

Citation

Joe, Harry. Majorization, Entropy and Paired Comparisons. Ann. Statist. 16 (1988), no. 2, 915--925. doi:10.1214/aos/1176350843. https://projecteuclid.org/euclid.aos/1176350843


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