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Statistical Decisions and Subjective Expected Utility: From Wald to Savage

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  • Ui, Takashi

Abstract

Waldʼs theory of statistical decision functions generalizes statistical estimation and hypotheses testing based upon game theory. Its main theorem is the complete class theorem, one of the earliest results that mathematically justify Bayesian decisions. Although the complete class theorem may appear to be related to Savageʼs subjective expected utility model, they are quite different in content and purpose. However, we can give an alternative axiomatic foundation for Anscombe and Aumannʼs subjective expected utility model using the complete class theorem and borrowing ideas from Nakada, Nitzan, Takeoka, and Ui（2020）; that is, we can connect Waldʼs theory to Savageʼs theory.

Suggested Citation

  • Ui, Takashi, 2021. "Statistical Decisions and Subjective Expected Utility: From Wald to Savage," Economic Review, Hitotsubashi University, vol. 72(2), pages 128-139, April.
    • Handle: RePEc:hit:ecorev:v:72:y:2021:i:2:p:128-139
    DOI: 10.15057/71667
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    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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