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Maximum likelihood estimation using composite likelihoods for closed exponential families

Author

Listed:
  • Kanti V. Mardia
  • John T. Kent
  • Gareth Hughes
  • Charles C. Taylor

Abstract

In certain multivariate problems the full probability density has an awkward normalizing constant, but the conditional and/or marginal distributions may be much more tractable. In this paper we investigate the use of composite likelihoods instead of the full likelihood. For closed exponential families, both are shown to be maximized by the same parameter values for any number of observations. Examples include log-linear models and multivariate normal models. In other cases the parameter estimate obtained by maximizing a composite likelihood can be viewed as an approximation to the full maximum likelihood estimate. An application is given to an example in directional data based on a bivariate von Mises distribution. Copyright 2009, Oxford University Press.

Suggested Citation

  • Kanti V. Mardia & John T. Kent & Gareth Hughes & Charles C. Taylor, 2009. "Maximum likelihood estimation using composite likelihoods for closed exponential families," Biometrika, Biometrika Trust, vol. 96(4), pages 975-982.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:4:p:975-982
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    File URL: http://hdl.handle.net/10.1093/biomet/asp056
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    Citations

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    Cited by:

    1. Bhat, Chandra R., 2011. "The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 923-939, August.
    2. Kenne Pagui, E.C. & Salvan, A. & Sartori, N., 2015. "On full efficiency of the maximum composite likelihood estimator," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 120-124.
    3. Paleti, Rajesh & Bhat, Chandra R., 2013. "The composite marginal likelihood (CML) estimation of panel ordered-response models," Journal of choice modelling, Elsevier, vol. 7(C), pages 24-43.
    4. Xibin Zhang & Maxwell L. King, 2011. "Bayesian semiparametric GARCH models," Monash Econometrics and Business Statistics Working Papers 24/11, Monash University, Department of Econometrics and Business Statistics.
    5. Kanti Mardia, 2010. "Bayesian analysis for bivariate von Mises distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 515-528.
    6. Xibin Zhang & Maxwell L. King, 2013. "Gaussian kernel GARCH models," Monash Econometrics and Business Statistics Working Papers 19/13, Monash University, Department of Econometrics and Business Statistics.
    7. Ranalli, Monia & Rocci, Roberto, 2017. "Mixture models for mixed-type data through a composite likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 87-102.
    8. Monia Ranalli & Roberto Rocci, 2024. "Composite likelihood methods for parsimonious model-based clustering of mixed-type data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(2), pages 381-407, June.
    9. T.-F. Lo & P.-H. Ke & W.-J. Tsay, 2018. "Pairwise likelihood inference for the random effects probit model," Computational Statistics, Springer, vol. 33(2), pages 837-861, June.
    10. Monia Ranalli & Roberto Rocci, 2017. "A Model-Based Approach to Simultaneous Clustering and Dimensional Reduction of Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1007-1034, December.
    11. Meisam Moghimbeygi & Mousa Golalizadeh, 2019. "A longitudinal model for shapes through triangulation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 99-121, March.

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