The Annals of Statistics

Special Capacities, the Hunt-Stein Theorem and Transformation Groups

Zbigniew Szkutnik

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Abstract

The problem of maximin testing between families of probability measures generated by special capacities and transformation groups is solved by showing that the Hunt-Stein theorem is applicable to such, generally nondominated, families of probability measures and that the problem reduces to maximin testing between neighbourhoods of distributions of maximal invariant, defined by special capacities closely related to the initial ones. An application to testing approximate binormality is also sketched.

Article information

Source
Ann. Statist., Volume 20, Number 2 (1992), 1120-1128.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348674

Digital Object Identifier
doi:10.1214/aos/1176348674

Mathematical Reviews number (MathSciNet)
MR1165610

Zentralblatt MATH identifier
0925.62017

JSTOR
links.jstor.org

Subjects
Primary: 62G35: Robustness
Secondary: 62A05 62C20: Minimax procedures 62H15: Hypothesis testing

Keywords
Special capacity Hunt-Stein theorem approximate binormality robust test

Citation

Szkutnik, Zbigniew. Special Capacities, the Hunt-Stein Theorem and Transformation Groups. Ann. Statist. 20 (1992), no. 2, 1120--1128. doi:10.1214/aos/1176348674. https://projecteuclid.org/euclid.aos/1176348674


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