Rate of strong consistency of the maximum quasi-likelihood estimator in quasi-likelihood nonlinear models

Quasi-likelihood nonlinear models (QLNM) include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation (MQLE) is obtained in QLNM. In an important case, this rate is O(n−1/2(loglogn)1/2), which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.