Pseudo-maximum likelihood method, adjusted pseudo-maximum likelihood method and covariance estimators

In this paper, we introduce an adjusted pseudo-maximum likelihood method. This procedure consists of solving centered pseudo-likelihood equations, i.e. equations in which the bias of the score function due to the misspecification is corrected by introducing terms involving its empirical mean. We show that these estimators may be considered as covariance estimators, i.e. estimators defined by means of some zero correlation constraints. These estimators are studied, especially their asymptotic properties and also their links with moment estimators.