On large-sample estimation and testing via quadratic inference functions for correlated data BY RAMANI S. PILLA AND CATHERINE LOADER

Hansen (1982) proposed the generalised method of moments (GMMs) for estimating a vector of regression parameters from a set of score functions. Hansen established that, under certain regularity conditions, the GMMs estimator is consistent, asymptotically normal, and asymptotically efficient. In the generalised estimating equation framework, Qu, Lindsay & Li (2000) extended the GMMs to create a quadratic inference function (QIF) that implicitly estimates the underlying correlation structure for the analysis of longitudinal data. The main goals of this research are to (1) provide an appropriate estimated covariance matrix for the set of extended score functions defining the inference functions; (2) establish a rigorous treatment of the large-sample properties of the QIF; (3) derive a generalisation of the QIF test for general linear hypotheses involving correlated data; and (4) propose an iterative reweighted generalised least squares algorithm for finding the QIF estimator.