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Non-Parametric Maximum Likelihood Density Estimation and Simulation-Based Minimum Distance Estimators

Author

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  • Gach, Florian
  • Pötscher, Benedikt M.

Abstract

Indirect inference estimators (i.e., simulation-based minimum distance estimators) in a parametric model that are based on auxiliary non-parametric maximum likelihood density estimators are shown to be asymptotically normal. If the parametric model is correctly specified, it is furthermore shown that the asymptotic variance-covariance matrix equals the Cramér-Rao bound. These results are based on uniform-in-parameters convergence rates and a uniform-in-parameters Donsker-type theorem for non-parametric maximum likelihood density estimators.

Suggested Citation

  • Gach, Florian & Pötscher, Benedikt M., 2010. "Non-Parametric Maximum Likelihood Density Estimation and Simulation-Based Minimum Distance Estimators," MPRA Paper 27512, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:27512
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    File URL: https://mpra.ub.uni-muenchen.de/27512/1/MPRA_paper_27512.pdf
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    References listed on IDEAS

    as
    1. Fermanian, Jean-David & Salanié, Bernard, 2004. "A Nonparametric Simulated Maximum Likelihood Estimation Method," Econometric Theory, Cambridge University Press, vol. 20(4), pages 701-734, August.
    2. Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
    3. Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 63-84, Suppl. De.
    4. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    5. Filippo Altissimo & Antonio Mele, 2009. "Simulated Non-Parametric Estimation of Dynamic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(2), pages 413-450.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Jean-Jacques Forneron, 2019. "A Sieve-SMM Estimator for Dynamic Models," Papers 1902.01456, arXiv.org, revised Jan 2023.

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    More about this item

    Keywords

    Indirect inference; simulation-based minimum distance estimation; non-parametric maximum likelihood; density estimation; efficiency;
    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
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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