Likelihood decision functions

Abstract

In both classical and Bayesian approaches, statistical inference is unified and generalized by the corresponding decision theory. This is not the case for the likelihood approach to statistical inference, in spite of the manifest success of the likelihood methods in statistics. The goal of the present work is to fill this gap, by extending the likelihood approach in order to cover decision making as well. The resulting likelihood decision functions generalize the usual likelihood methods (such as ML estimators and LR tests), while maintaining some of their key properties, and thus providing a theoretical foundation for established and new likelihood methods.