Graph-based estimators for paired comparison data

Sayan Ghosh, Ori Davidov

Research output: Contribution to journalArticlepeer-review


Paired comparison data is often used to rank or order a set of items. In this paper we study a method for estimating the parameters associated with completely ordered cardinal paired comparison data. The analysis is carried out within the framework of graphical linear models but rather than using the least squares estimator, which may be difficult to analyze, we consider the average of all tree-based estimators for the connected comparison graph. The resulting estimator is a simple linear function of the sufficient statistics and has an easy to understand graph-theoretic interpretation. The statistical properties of this estimator are studied and it is shown to be unbiased, strongly consistent and asymptotically normal. Examples and numerical comparisons are provided and extensions are discussed.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalJournal of Statistical Planning and Inference
StatePublished - Dec 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.


  • Incidence matrix
  • Moore–Penrose inverse
  • Paired comparisons
  • Spanning tree
  • Statistical ranking

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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