An Alternative Derivation of Weak Convergence Concerning Quasi-likelihood Estimation with an Application in Simultaneous Inference 

Often arises in counting data analysis that both violation of distributional assumption and large-scale over-dispersion substantially impair the validity of the methods for multiple comparisons. For over- dispersed data fitting to the generalized linear models, in this talk, we describe the simultaneous inference method in assessing a sequence of estimable functions based on the root using the quasi- likelihood estimation of the regression coefficients. We present a new method for deriving the limiting distributions of the score function and the root under a list of mild regularity conditions. This approach has a close connection to the asymptotic normality of the root based on the least squares estimation of regression coefficients in general linear models. Hence, researchers can routinely estimate quantiles based on the limiting distribution of the root for simultaneous inference. We apply the proposed method to a real example from an antibiotic trial, where the data presents a large-degree of over- dispersion.