Fourth order pseudo maximum likelihood methods
AbstractThe 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 InfoPaper provided by University of Lausanne, Institute of Health Economics and Management (IEMS) in its series Working Papers with number 0802.
Length: 42 pages
Date of creation: Aug 2008
Date of revision:
Quartic Exponential Family; Pseudo Maximum Likelihood; Skewness; Kurtosis;
Other versions of this item:
- Alberto HOLLY & Alain MONFORT & Michael ROCKINGER, . "Fourth Order Pseudo Maximum Likelihood Methods," Swiss Finance Institute Research Paper Series 09-23, Swiss Finance Institute.
- Alberto HOLLY & Alain MONFORT & Michael ROCKINGER, 2011. "Fourth Order Pseudo Maximum Likelihood Methods," Working Papers 2011-05, Centre de Recherche en Economie et Statistique.
- Alberto Holly & Alain Monfort & Michael Rockinger, 2011. "Fourth order pseudo maximum likelihood methods," Post-Print peer-00815562, HAL.
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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