Applications of Choquet expected utility to hypothesis testing with incompleteness

Abstract

The Maximin and Choquet expected utility theories guide decision-making under ambiguity. We apply them to hypothesis testing in incomplete models. We consider a statistical risk function that uses a prior probability to incorporate parameter uncertainty and a belief function to reflect the decision-maker’s willingness to be robust against the model’s incompleteness. We develop a numerical method to implement a test that minimizes the risk function. We also use a sequence of such tests to approximate a minimax optimal test when a nuisance parameter is present under the null hypothesis.