The Annals of Statistics

Sequential Bahadur Efficiency

Robert H. Berk and L. D. Brown

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Abstract

The notion of Bahadur efficiency for test statistics is extended to the sequential case and illustrated in the specific context of testing one-sided hypotheses about a normal mean. An analog of Bahadur's theorem on the asymptotic optimality of the likelihood ratio statistic is seen to hold in the normal case. Some possible definitions of attained level for a sequential experiment are considered.

Article information

Source
Ann. Statist., Volume 6, Number 3 (1978), 567-581.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344201

Digital Object Identifier
doi:10.1214/aos/1176344201

Mathematical Reviews number (MathSciNet)
MR468064

Zentralblatt MATH identifier
0403.62055

JSTOR
links.jstor.org

Subjects
Primary: 62L10: Sequential analysis
Secondary: 62F20 62F05: Asymptotic properties of tests 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 62E20: Asymptotic distribution theory

Keywords
Bahadur efficiency Bahadur index attained level sequential test stopping time

Citation

Berk, Robert H.; Brown, L. D. Sequential Bahadur Efficiency. Ann. Statist. 6 (1978), no. 3, 567--581. doi:10.1214/aos/1176344201. https://projecteuclid.org/euclid.aos/1176344201


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