On asymptotic quasi-likelihood estimation

Ordinary quasi-likelihood estimators are based on estimating functions with certain strong orthogonality properties. Asymptotic quasi-likelihood (AQL) estimators, introduced herein correspond to the case where the orthogonality results hold asymptotically but yet the estimators enjoy the same kind of properties as ordinary quasi-likelihood estimators, such as having asymptotic confidence zones of minimum size. The methodology is illustrated through a discussion of the estimation procedure based on smoothed periodograms and the demonstration that the Whittle procedure often has the AQL property.