Modified Wald statistics for generalized linear models

Summary: Wald statistics in generalized linear models are asymptotically ² distributed.The asymptotic chi–squared law of the corresponding quadratic form shows disadvantageswith respect to the approximation of the finite–sample distribution. It is shown by meansof a comprehensive simulation study that improvements can be achieved by applyingsimple finite–sample size approximations to the distribution of the quadratic form ingeneralized linear models. These approximations are based on a ² distribution with anestimated degree of freedom that generalizes an approach by Patnaik and Pearson. Simulation studies confirm that nominal level is maintained with higher accuracy comparedto the Wald statistics.