Under broadly applicable conditions, quasi-likelihood estimators are consistent and asymptotically normal.
Examples of quasi-likelihood methods include the generalized estimating equations and pairwise likelihood approaches.
Quasi-likelihood estimation is one way of allowing for overdispersion, that is, greater variability in the data than would be expected from the statistical model used.
Most commonly, the variance function is of a form such that fixing the overdispersion parameter at unity results in the variance-mean relationship of an actual probability distribution such as the binomial or Poisson.
Quasi-likelihood methods have the advantage of relative computational simplicity, speed and robustness, as they can make use of the more straightforward algorithms developed to fit generalized linear models.