Please cite this article as: Holly, A., Monfort, A., Rockinger, M., Fourth order pseudo maximum likelihood methods. Journal of Econometrics (2011Econometrics ( ), doi:10.1016Econometrics ( /j.jeconom.2011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Milovanović for providing a very useful sequence of parameters used for numerical integrations.
A C C E P T E D M A N U S C R I P T
A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT
AbstractWe 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.