Simultaneous confidence intervals of estimable functions based on quasi-likelihood in generalized linear models for over-dispersed data

Two major problems besetting count data analysis in multiple comparisons are over-dispersion and violation of distributional assumptions of real data. In this article, we describe the simultaneous confidence interval method to inference a collection of estimable functions in generalized linear models based on quasi-likelihood estimation. We assume that the independent observations have the variance proportional to a given function of the mean. We define the pivotal quantities in an asymptotic sense. We derive the joint limiting distribution of the pivotal quantities and the asymptotic distribution of the maximum modulus statistic. In the presence of over-dispersion, large-sample approximation method is shown to be liberal in multiple comparisons. We propose a percentile-tbootstrap method based on Pearson residuals as a robust alternative. It shows that the proposed method outperforms large-sample approximation method in the spirit of attaining the overall coverage probability, even when the working variance-mean structure moderately deviates from the real structure of the underlying distribution.