The Annals of Statistics

Locally Most Powerful Sequential Tests

Robert H. Berk

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Abstract

Sequential tests that are LMP for certain one-sided testing problems are discussed. In all cases considered, the stopping rule is the first time a certain random walk leaves a bounded interval. (Thus various inequalities and approximations due to Wald can be utilized in obtaining properties of these tests.) For models in a one-parameter exponential family, each LMP sequential test is shown to be a Wald SPRT for a family of paired (conjugate) simple hypotheses.

Article information

Source
Ann. Statist., Volume 3, Number 2 (1975), 373-381.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343063

Digital Object Identifier
doi:10.1214/aos/1176343063

Mathematical Reviews number (MathSciNet)
MR368346

Zentralblatt MATH identifier
0332.62063

JSTOR
links.jstor.org

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

Keywords
Sequential analysis sequential test locally most powerful test SPRT exponential models conjugate parameter pairs optimal stopping

Citation

Berk, Robert H. Locally Most Powerful Sequential Tests. Ann. Statist. 3 (1975), no. 2, 373--381. doi:10.1214/aos/1176343063. https://projecteuclid.org/euclid.aos/1176343063


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