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Consistent Pseudo-Maximum Likelihood Estimators


  • Christian Gouriéroux
  • Alain Monfort
  • Eric Renault


The development of the literature on the pseudo maximum likelihood (PML) estimators would not have been so efficient without the modern proof of consistency of extremum estimators introduced at the end of the sixties by E. Malinvaud and R. Jennrich. We discuss this proof and replace it in an historical perspective. In this paper we also provide a survey of the literature on consistent (PML) estimators. We emphasize the role of the white noise assumptions on the set of pseudo distributions leading to consistent estimators. The stronger these assumptions, the larger the set of consistent PML estimators. We also illustrate the importance of these PML approaches in big data environment.

Suggested Citation

  • Christian Gouriéroux & Alain Monfort & Eric Renault, 2017. "Consistent Pseudo-Maximum Likelihood Estimators," Annals of Economics and Statistics, GENES, issue 125-126, pages 187-218.
  • Handle: RePEc:adr:anecst:y:2017:i:125-126:p:187-218

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    References listed on IDEAS

    1. Hsiao, Cheng & Kim, Changseob & Taylor, Grant, 1990. "A statistical perspective on insurance rate-making," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 5-24.
    2. Gouriéroux, Christian & Monfort, Alain & Renne, Jean-Paul, 2017. "Statistical inference for independent component analysis: Application to structural VAR models," Journal of Econometrics, Elsevier, vol. 196(1), pages 111-126.
    3. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    4. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    5. Crouhy, Michel & Galai, Dan & Mark, Robert, 2000. "A comparative analysis of current credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 59-117, January.
    6. Gourieroux, C. & Monfort, A., 2018. "Composite indirect inference with application to corporate risks," Econometrics and Statistics, Elsevier, vol. 7(C), pages 30-45.
    7. N/A, 1990. "Statistical Appendix," National Institute Economic Review, National Institute of Economic and Social Research, vol. 132(1), pages 93-102, May.
    8. Michael L. Stein & Zhiyi Chi & Leah J. Welty, 2004. "Approximating likelihoods for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 275-296, May.
    9. N/A, 1990. "Statistical Appendix," National Institute Economic Review, National Institute of Economic and Social Research, vol. 131(1), pages 91-100, February.
    10. Francq, Christian & Lepage, Guillaume & Zakoïan, Jean-Michel, 2011. "Two-stage non Gaussian QML estimation of GARCH models and testing the efficiency of the Gaussian QMLE," Journal of Econometrics, Elsevier, vol. 165(2), pages 246-257.
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    Cited by:

    1. Gouriéroux, Christian & Monfort, Alain & Zakoian, Jean-Michel, 2017. "Pseudo-Maximum Likelihood and Lie Groups of Linear Transformations," MPRA Paper 79623, University Library of Munich, Germany.

    More about this item


    Pseudo-Likelihood; Composite Pseudo-Likelihood; Consistency; Big Data; ARCH Model; Normalized Data; Lie Group;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis


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