Asymptotic Quasi-Likelihood

Abstract

Discussion in earlier chapters on optimality of estimating functions and quasi-likelihood has been concerned with exact results, where a specific criterion holds for either fixed T or for each T as T → ∞. Here we address the situation where the criteria for optimality are not satisfied exactly but hold in a certain asymptotic sense to be made precise below. These considerations give rise to an equivalence class of asymptotic quasi-likelihood estimator, which enjoy the same kind of properties as ordinary quasi-likelihood estimators, such as having asymptotic confidence zones of minimum size, within a specified family, for the “parameter” in question.