Autori
Schervish, Mark J.
Seidenfeld, Teddy
Kadane, Joseph B.
Stern, Rafael B.

Titolo
What finite-additivity can add to decision theory
Periodico
Statistical methods & applications : Journal of the Italian Statistical Society
Anno: 2020 - Volume: 29 - Fascicolo: 2 - Pagina iniziale: 237 - Pagina finale: 263

We examine general decision problems with loss functions that are bounded below. We allow the loss function to assume the value ∞. No other assumptions are made about the action space, the types of data available, the types of non-randomized decision rules allowed, or the parameter space. By allowing prior distributions and the randomizations in randomized rules to be finitely-additive, we prove very general complete class and minimax theorems. Specifically, under the sole assumption that the loss function is bounded below, we show that every decision problem has a minimal complete class and all admissible rules are Bayes rules. We also show that every decision problem has a minimax rule and a least-favorable distribution and that every minimax rule is Bayes with respect to the least-favorable distribution. Some special care is required to deal properly with infinite-valued risk functions and integrals taking infinite values.



SICI: 1618-2510(2020)29:2<237:WFCATD>2.0.ZU;2-3

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