Laws of iterated logarithm for quasi-maximum likelihood estimator in generalized linear model

For the case that the expectation of the response variable Y   is correctly specified in the generalized linear model (GLM), under some regular assumptions, we obtain and prove the law of the iterated logarithm and Chung type law of the iterated logarithm for the quasi-maximum likelihood estimator (QMLE) βnβn in this model.