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Models on Spheres and Models for Permutations

  • Peter McCullagh
Part of the Lecture Notes in Statistics book series (LNS, volume 80)

Abstract

It is shown that the space of permutations is naturally ordered in a circular or spherical manner. By exploiting the geometry of the sample space it is shown that Mallows’s ϕ-model with the Spearman metric is essentially equivalent to the Mallows-Bradley-Terry ranking model, which is essentially equivalent to the von Mises-Fisher model on the sphere. Extensions to bi-polar models are discussed briefly. References

Keywords

Sample Space Ordinal Number Exponential Family Ranking Model Rank Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Mallows, C.L. Non-Null Ranling Models. I. Biometrika 44:114–130, 1957.MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1993

Authors and Affiliations

  • Peter McCullagh
    • 1
  1. 1.Department of StatisticsUniversity of ChicagoUSA

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