Statistical Papers

, Volume 60, Issue 6, pp 1883–1919 | Cite as

On divergence tests for composite hypotheses under composite likelihood

  • N. Martín
  • L. Pardo
  • K. ZografosEmail author
Regular Article


It is well-known that in some situations it is not easy to compute the likelihood function as the datasets might be large or the model is too complex. In that contexts composite likelihood, derived by multiplying the likelihoods of subjects of the variables, may be useful. The extension of the classical likelihood ratio test statistics to the framework of composite likelihoods is used as a procedure to solve the problem of testing in the context of composite likelihood. In this paper we introduce and study a new family of test statistics for composite likelihood: Composite \(\phi \) -divergence test statistics for solving the problem of testing a simple null hypothesis or a composite null hypothesis. To do that we introduce and study the asymptotic distribution of the restricted maximum composite likelihood estimate.


Composite likelihood Maximum composite likelihood estimator Restricted maximum composite likelihood estimator Composite likelihood \(\phi \)-divergence test-statistics 

Mathematics Subject Classification

62F03 62F05 62F30 62B10 



The authors would like to thank the referees for their helpful comments and suggestions. The third author wants to cordially thank Prof. Alex de Leon, from the University of Calgary, for fruitful discussions on composite likelihood methods, some years ago. This research is partially supported by Grant MTM2015-67057-P from Ministerio de Economia y Competitividad (Spain).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Statistics and O.R. IIComplutense University of MadridMadridSpain
  2. 2.Department of Statistics and O.R. IComplutense University of MadridMadridSpain
  3. 3.Department of MathematicsUniversity of IoanninaIoanninaGreece

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