Robust Second-Order Accurate Inference for Generalized Linear Models

Generalized linear models have become the most commonly used class of regression models in the analysis of a large variety of data. In particular, generalized linear model can be used to model the relationship between predictors and a function of the mean of a continuous or discrete response variable. The estimation of the parameters of the model can be carried out by maximum likelihood or quasi-likelihood methods, which are equivalent if the link is canonical. Standard asymptotic inference based on likelihood ratio, Wald and score test is then readily available for these models. However, two main problems can potentially invalidate p-values and confidence intervals based on standard classical techniques. First of all, the models are ideal approximations to reality and deviations from the assumed distribution can have important effects on classical estimators and tests for these models (nonro-bustness). Secondly, even when the model is exact, standard classical inference is based on (first order) asymptotic theory. This can lead to inaccurate p-values and confidence intervals when the sample size is moderate to small or when probabilities in the extreme tails are required