Les méthodes du pseudo-maximum de vraisemblance

This article brings together a lot of essential principles about the pseudo-likelihood methods. The proofs of the results are not presented here since they have been developped in a previous serie of papers. On the contrary our aim is to insist on the intuitive motivations and to illustrate some results by examples. The consistent estimation of the parameters of interest involved in the conditionnal expectation of the endogenous variables upon the exogenous ones rests on the linear exponential family. For these types of estimators there exists an optimal bound for the asymptotic variance that can be achieved by the implementation of the quasi-generalised pseudo-maximum likelihood method. It is shown at the end of the paper that asymptotic tests based on the pseudo-likelihood function can be used for classical inference. Those tests are analogous to the Wald, Lagrange and in some cases to the likelihood ratio tests built on the likelihood function.