Some robustness properties of the Fisher combined test

Abstract

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. In particular, it maximizes the Bahadur exact slope in a quite general class of robust Fisher's combinations.