Sankhya: The Indian Journal of Statistics

1995, Volume 57, Series A, Pt. 3, pp. 424--432

 STEIN'S PARADOX AND STEPWISE BAYES RULES

By

  M. ASGHARIAN and S. NOORBALOOCHI, Shaheed Behesti University

SUMMARY.   For a decision problem with a finite parameter space, Hsuan (1979) proved that the set of unique stepwise Bayes rule is a minimal complete class. In this paper, using an algorithm with infinitely many steps we show that for an arbitrary parameter space, any unique stepwise Bayes rule is admissible, Stein paradox is impossible for unique stepwise Bayes rules. In the language of Gutmann (1984), such unique stepwise Bayes rules are superimmune. As examples, admissibility aand superimmunity of some estimators for population size of a Hypergeometric, discrete extremal and binomial probability functions are demonstrated.

AMS (1991) subject classification.   Primary 62C15, secondary 62D05.

Key words and phrases. Admissibility, stepwise Bayes rules, Stein's paradox, immunity, superimmunity size of a closed population.

Full paper (PDF)

This article in mathematical reviews.