Generalized Quasi - likelihood ( GQL ) Inference

QL Estimation for Independent Data. For i = 1, . . . ,K, let Yi denote the response variable for the ith individual, and xi = (xi1, . . . , xiv , . . . , xip) ′ be the associated p−dimensional covariate vector. Also, let β be the p−dimensional vector of regression effects of xi on yi. Further suppose that the responses are collected from K independent individuals. It is understandable that if the probability distribution of Yi is not known, then one can not use the well known likelihood approach to estimate the underlying regression parameter β. Next suppose that only two moments of the data, that is, the mean and the variance functions of the response variable Yi for all i = 1, . . . ,K, are known, and for a known functional form a(·), these moments are given by