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Conditionally acceptable frequentist solutions. (English) Zbl 0653.62004

Statistical decision theory and related topics IV, Pap. 4th Purdue Symp., West Lafayette/Indiana 1986, Vol. 1, 73-117 (1988).
[For the entire collection see Zbl 0638.00031.]
Noting that traditional frequentist criteria alone may lead to statistical procedures suffering from poor conditional behaviour, the author proposes a conditional frequentist criterion which is based on a theory of relevant betting strategies. Stronger conditional criteria than those hitherto given are presented and illustrated by several examples. Conditionally acceptable procedures are discussed, and pre-trial behaviour is contrasted with post-data interpretation. The betting-based theory advocated here is, it is claimed, “a reasonable augmentation of frequentist theory” (p. 74). Alternative approaches, and criticism, are presented in the extensive discussion papers which follow the author’s presentation.
Reviewer: A.Dale

MSC:

62A01 Foundations and philosophical topics in statistics
62F15 Bayesian inference
62F25 Parametric tolerance and confidence regions

Citations:

Zbl 0638.00031