The Annals of Statistics

Asymptotic Efficiencies of Sequential Tests

Robert H. Berk

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Abstract

Some concepts of relative and absolute efficiency for sequential tests are considered. These are sequential analogs of Hodges-Lehmann and Chernoff efficiencies. Using these criteria, several sequential tests for the mean of a normal distribution are evaluated. Among them are Wald's SPRT, Anderson's triangular boundary, Bayes and APO tests and a repeated significance test. Truncated versions of these tests are also considered. Asymptotic expressions for the (expected) stopping times and error rates are given.

Article information

Source
Ann. Statist., Volume 4, Number 5 (1976), 891-911.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343587

Digital Object Identifier
doi:10.1214/aos/1176343587

Mathematical Reviews number (MathSciNet)
MR418368

Zentralblatt MATH identifier
0374.62076

JSTOR
links.jstor.org

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

Keywords
Sequential test asymptotic efficiency SPRT truncated sequential test Anderson's boundaries APO test Bayes sequential test repeated significance test Wiener process

Citation

Berk, Robert H. Asymptotic Efficiencies of Sequential Tests. Ann. Statist. 4 (1976), no. 5, 891--911. doi:10.1214/aos/1176343587. https://projecteuclid.org/euclid.aos/1176343587


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