Empirical Likelihood and Ranking Methods

  • Mayer AlvoEmail author
Part of the Fields Institute Communications book series (FIC, volume 76)


Empirical likelihood methods are applied to various problems in two-way layouts involving the use of ranks. It is shown that the resulting test statistics are asymptotically equivalent to well known statistics such as the Friedman test for concordance. Generalizations and applications to the multi-sample situation are presented.


Empirical Likelihood Balance Incomplete Block Design Narrow Confidence Interval Empirical Likelihood Method Empirical Likelihood Ratio 
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.



Work supported by Natural Sciences and Engineering Council of Canada Grant OGP0009068.


  1. 1.
    Aitchison, J., Silvey, S.D.: Maximum-likelihood estimation of parameters subject to restraints. Ann. Math. Stat. 29, 813–828 (1958)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Alvo, M., Cabilio, P.: A general rank based approach to the analysis of block data. Commun. Stat. Theory Methods 28, 197–215 (1999)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Alvo, M., Cabilio, P., Feigin, P.D.: Asymptotic theory for measures of concordance with special reference to average Kendall tau. Ann. Stat. 10, 1269–1276 (1982)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Boos, D.D.: On generalized score tests. Am. Stat. 46, 327–333 (1992)Google Scholar
  5. 5.
    DiCiccio, T.J., Hall, P., Romano, J.: Empirical likelihood is Bartlett-correctable. Ann. Stat. 19, 1053–1061 (1991)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Feigin, P.D., Alvo, M.: Intergroup diversity and concordance for ranking data: an approach via metrics for permutations. Ann. Stat. 14, 691–707 (1986)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Iman, R.L., Davenport, J.M.: Approximations of the critical region of the Friedman statistic. Commun. Stat. Theory Methods A9(6), 571–595 (1980)zbMATHCrossRefGoogle Scholar
  8. 8.
    Jensen, D.R.: On approximating the distribution of Friedman’s χ 2. Metrika 24, 75–85 (1977)zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Liu, T., Yuan, X., Lin, N., Zhang, B.: Rank-based empirical likelihood inference on medians of k populations. J. Stat. Plan. Inference 142, 1009–1026 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Neyman, J., Scott, E.: Note on techniques of evaluation of single rain stimulations experiments. In: Proceedings of the Fifth Berkeley Symposium vol. 5, pp. 327–350. University of California Press, Berkeley (1967)Google Scholar
  11. 11.
    Owen, A.B.: Empirical Likelihood. Chapman & Hall/CRC, Boca Raton (2001)zbMATHCrossRefGoogle Scholar
  12. 12.
    Qin, J., Lawless, J.F.: Estimating equations, empirical likelihood and constraints on parameters. Can. J. Stat. 23, 145–159 (1995)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Sen, P.K.: Asymptotically efficient tests by the method of n rankings. J. R. Stat. Soc. B 30, 312–317 (1968)zbMATHGoogle Scholar

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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada

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