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Fourth order pseudo maximum likelihood methods

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  • Alberto Holly

    ()
    (Faculty of Business and Economics - University of Lausanne)

  • Alain Monfort

    ()

  • Michael Rockinger

    ()
    (University of Lausanne - University of Lausanne)

Abstract

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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Bibliographic Info

Paper provided by HAL in its series Post-Print with number peer-00815562.

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Date of creation: 19 Apr 2011
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Publication status: Published, Journal of Econometrics, 2011
Handle: RePEc:hal:journl:peer-00815562

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Related research

Keywords: C01; C13; C16; C22; Quartic exponential family; Pseudo maximum likelihood; Skewness; Kurtosis;

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Cited by:
  1. Giuseppe arbia, 2014. "Least quartic Regression Criterion with Application to Finance," Papers 1403.4171, arXiv.org.

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