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December, 1993 A Note on Bahadur's Transitivity
Eitan Greenshtein
Ann. Statist. 21(4): 2163-2167 (December, 1993). DOI: 10.1214/aos/1176349417

Abstract

Let $X_1, X_2, \cdots$ be a sequence of random variables, $(X_1, \cdots, X_n) \sim F^n_\theta, \theta \in \Theta$. In a work by Bahadur it was shown that, for some sequential problems, an inference may be based on a sequence of sufficient and transitive statistics $S_n = S_n(X_1, \cdots, X_n)$ without any loss in statistical performance. A simple criterion for transitivity is given in Theorem 1.

Citation

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Eitan Greenshtein. "A Note on Bahadur's Transitivity." Ann. Statist. 21 (4) 2163 - 2167, December, 1993. https://doi.org/10.1214/aos/1176349417

Information

Published: December, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0799.62088
MathSciNet: MR1245788
Digital Object Identifier: 10.1214/aos/1176349417

Subjects:
Primary: 62L10
Secondary: 62B99

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 4 • December, 1993
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