In this note we study the behavior of maximum quasilikelihood estimators (MQLEs) for a class of statistical models, in which only knowledge about the first two moments of the response variable is assumed. This class includes, but is not restricted to, generalized linear models with general link function. Our main results are related to guarantees on existence, strong consistency and mean square convergence rates of MQLEs. The rates are obtained from first principles and are stronger than known a.s. rates. Our results find important application in sequential decision problems with parametric uncertainty arising in dynamic pricing. Keywords: Quasi-likelihood estimation, strong consistency, mean square convergence rates.