Likelihood-Based Statistical Decisions
Marco Cattaneo · 2005
In this paper, a nonadditive quantitative description of uncertain knowledge about statistical models is ob-tained by extending the likelihood function to sets and allowing the use of prior information. This descrip-tion, which has the distinctive feature of not being calibrated, is called relative plausibility. It can be updated when new information is obtained, and it can be used for inference and decision making. As re-gards inference, the well-founded theory of likelihood-based statistical inference can be exploited, whereas decisions can be based on the minimax plausibility-weighted loss criterion. In the present paper, this de-cision criterion is introduced and some of its proper-ties are studied, both from the conditional and from the repeated sampling point of view.