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Fourth Order Pseudo Maximum Likelihood Methods

  • Alberto HOLLY


  • Alain MONFORT


  • Michael ROCKINGER


We extend PML theory to account for information on the conditional moments up to order four, but without assuming a parametric model, to avoid a risk of misspecification of the conditional distribution. The key statistical tool is the quartic exponential family, which allows us to generalize the PML2 and QGPML1 methods proposed in Gourieroux, Monfort, and Trognon (1984) to PML4 and QGPML2 methods, respectively. An asymptotic theory is developed. The key numerical tool that we use is the Gauss-Freud integration scheme that solves a computational problem that has previously been raised in several fields. Simulation exercises demonstrate the feasibility and robustness of the methods.

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Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2011-05.

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Date of creation: 2011
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Handle: RePEc:crs:wpaper:2011-05
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  10. Altonji, Joseph G & Segal, Lewis M, 1996. "Small-Sample Bias in GMM Estimation of Covariance Structures," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 353-66, July.
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