Some robustness properties of the Fisher combined test

A. Pallini
Robustness of the Fisher combined test is investigated via Lambert's influence function for P-values. It is well known that this influence function is defined in terms of Bahadur exact slope. The classical Fisher method of combining independent P-values is asymptotically Bahadur optimal in a reasonable class of combinations of tests. A robust version for the Fisher combined test is proposed. This robust test is shown to still have an optimality property in the Bahadur sense....