Econometrica Vol. 52 No. 3 1984

Pseudo Maximum Likelihood Methods: Theory

C. Gouriéroux; Alain Monfort^1,2,3; Alain Trognon^1,2,3

¹ Centre Pour La Recherche Economique et ses Applications · ² Université Paris Dauphine-PSL · ³ ENSAE Paris

Abstract

Estimators obtained by maximizing a likelihood function are studied in the case where the true p.d.f. does not necessarily belong to the family chosen for the likelihood function. When such a procedure is applied to the estimation of the parameters of the first order moments, it is possible to prove a necessary and sufficient condition for its consistency. Asymptotic normality is shown as well as the existence of a lower bound for the asymptotic covariance matrix. It is also seen that this bound can be reached if consistent estimates are available for the parameters of the second order moments. Finally, a necessary and sufficient condition for the consistency if the pseudo maximum likelihood estimation of the first and second moments is given.

DOI

10.2307/1913471

Volume

52

Issue

3

Pages

681

Sources

bibtex:phds-export.bib openalex crossref

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