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Consistent Pseudo-Maximum Likelihood Estimators

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  • Christian Gouriéroux
  • Alain Monfort
  • Eric Renault

Abstract

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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    File URL: http://www.jstor.org/stable/10.15609/annaeconstat2009.125-126.0187
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    References listed on IDEAS

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    13. 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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    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.
    2. Moreno Bevilacqua & Christian Caamaño‐Carrillo & Reinaldo B. Arellano‐Valle & Víctor Morales‐Oñate, 2021. "Non‐Gaussian geostatistical modeling using (skew) t processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 212-245, March.

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    More about this item

    Keywords

    Pseudo-Likelihood; Composite Pseudo-Likelihood; Consistency; Big Data; ARCH Model; Normalized Data; Lie Group;
    All these keywords.

    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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