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MINIMAX, INFORMATION AND ULTRAPESSIMISM
PARMIGIANI G
THEORY AND DECISION 33 (3): 241-252 NOV 1992

Document type: Article

Language: English

Cited References: 9

Times Cited: 0

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.

Author Keywords:
MINIMAX PRINCIPLE, REGRET, SEQUENTIAL STATISTICAL DECISIONS, INFORMATION, IDENTIFIABILITY, LEAST FAVORABLE DISTRIBUTIONS, ULTRAPESSIMISM

Addresses:
PARMIGIANI G, DUKE UNIV,INST STAT & DECIS SCI,DURHAM,NC 27708

Publisher:
KLUWER ACADEMIC PUBL, DORDRECHT

IDS Number:
KD609

ISSN:
0040-5833

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