Strong consistency of maximum quasi-likelihood estimates in generalized linear models

In a generalized linear model with q× 1 responses, bounded and fixed p × q regressors Z_i and general link function, under the most general assumption on the minimum eigenvalue of the moment condition on responses as weak as possible and other mild regular conditions, we prove that with probability one, the quasi-likelihood equation has a solution _n for all large sample size n, which converges to the true regression parameter β₀. This result is an essential improvement over the relevant results in literature.