Minimax, information and ultrapessimism

Giovanni Parmigiani

Research output: Contribution to journalArticlepeer-review

Abstract

Discussing the foundations of the minimax principle, Savage (1954) argued that it is "utterly untenable for statistics" because it is "ultrapessimistic" when applied to negative income, but claimed that such objection is not relevant when the principle is applied to regret. In this paper I rebut the latter claim. I first present an example where ultrapessimism, as Savage understood it, applies to minimax regret but not to minimax negative income. Then, for a sequential decision problems with two terminal acts and a finite number of states of nature, I give necessary and sufficient conditions for a decision rule to be ultrapessimistic, and show that for every payoff table with at least three states, be it in regret form or not, there exist an experiment such that the minimax rule is ultrapessimistic. I conclude with some more general remarks on information and the value of experimentation for a minimax agent.

Original languageEnglish (US)
Pages (from-to)241-252
Number of pages12
JournalTheory and Decision
Volume33
Issue number3
DOIs
StatePublished - Nov 1992
Externally publishedYes

Keywords

  • identifiability
  • information
  • least favorable distributions
  • Minimax principle
  • regret
  • sequential statistical decisions
  • ultrapessimism

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics

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