Pseudo Maximum Likelihood Methods: Theory

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...

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Bibliographic Details
Published in:Econometrica 1984-05, Vol.52 (3), p.681-700
Main Authors: Gourieroux, C., Monfort, A., Trognon, A.
Format: Article
Language:English
Subjects:
Binomials
Consistent estimators
Covariance matrices
Economic models
Equality
Estimation methods
Estimation theory
Estimators
Laplace transforms
Mathematical moments
Maximum likelihood estimation
Maximum likelihood estimators
Maximum likelihood method
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Summary: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.
ISSN:0012-9682
1468-0262
DOI:10.2307/1913471