The connection between quasi-likelihood functions, exponential family models and nonlinear weighted least squares is examined. Consistency and asymptotic normality of the parameter estimates are discussed under second moment assumptions. The parameter estimates are shown to satisfy a property of asymptotic optimality similar in spirit to, but more general than, the corresponding optimal property of Gauss-Markov estimators.
Peter McCullagh. "Quasi-Likelihood Functions." Ann. Statist. 11 (1) 59 - 67, March, 1983. https://doi.org/10.1214/aos/1176346056