Translator Disclaimer
June, 1994 Recursive Testing of Multiple Hypotheses: Consistency and Efficiency of the Bayes Rule
Andrew L. Rukhin
Ann. Statist. 22(2): 616-633 (June, 1994). DOI: 10.1214/aos/1176325487

Abstract

A version of the multiple hypotheses testing problem is studied in which the decision procedure is based only on the current observation and the previous decision. Conditions for inconsistency and consistency of the stepwise Bayes rule, which are related to the boundedness of the likelihood ratios, are given. The (typically slow) rate of convergence of the error probabilities of consistent procedures is determined, and a sharp lower bound for the Bayes risk in terms of bounds on the likelihood ratios is derived. A modification of the recursive Sakrison's procedure for a continuous estimation problem is obtained in this setting by embedding the discrete family of original probability distributions into an exponential family.

Citation

Download Citation

Andrew L. Rukhin. "Recursive Testing of Multiple Hypotheses: Consistency and Efficiency of the Bayes Rule." Ann. Statist. 22 (2) 616 - 633, June, 1994. https://doi.org/10.1214/aos/1176325487

Information

Published: June, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0815.62009
MathSciNet: MR1292532
Digital Object Identifier: 10.1214/aos/1176325487

Subjects:
Primary: 62F05
Secondary: 62E20, 62F12

Rights: Copyright © 1994 Institute of Mathematical Statistics

JOURNAL ARTICLE
18 PAGES


SHARE
Vol.22 • No. 2 • June, 1994
Back to Top