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Fourth order pseudo maximum likelihood methods

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Author Info

  • Alberto Holly
  • Alain Montfort
  • Michael Rockinger

Abstract

The objective of this paper is to extend the results on Pseudo Maximum Likelihood (PML) theory derived in Gourieroux, Monfort, and Trognon (GMT) (1984) to a situation where the first four conditional moments are specified. Such an extension is relevant in light of pervasive evidence that conditional distributions are non-Gaussian in many economic situations. The key statistical tool here is the quartic exponential family, which allows us to generalize the PML2 and QGPML1 methods proposed in GMT(1984) to PML4 and QGPML2 methods, respectively. An asymptotic theory is developed which shows, in particular, that the QGPML2 method reaches the semi-parametric bound. The key numerical tool that we use is the Gauss-Freud integration scheme which solves a computational problem that has previously been raised in several econometric fields. Simulation exercises show the feasibility and robustness of the methods.

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Bibliographic Info

Paper provided by University of Lausanne, Institute of Health Economics and Management (IEMS) in its series Working Papers with number 0802.

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Length: 42 pages
Date of creation: Aug 2008
Date of revision:
Handle: RePEc:hem:wpaper:0802

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Related research

Keywords: 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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