Determining the mean–variance relationship in generalized linear models—A parametric robust way

This article introduces a parametric robust way of determining the mean–variance relationship in the setting of generalized linear models. More specifically, the normal likelihood is properly amended to become asymptotically valid even if normality fails. Consequently, legitimate inference for the parametric relationship between mean and variance could be derived under model misspecification. More details are given to the scenario when the variance is proportional to an unknown power of the mean function. The efficacy of the novel technique is demonstrated via simulations and the analysis of two real data sets.