The Annals of Statistics

Nonnull and Optimality Robustness of Some Tests

Takeaki Kariya and Bimal Kumar Sinha

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Abstract

This paper first characterizes the invariant structure of a model for which nonnull robustness holds. Applications of this result yield the nonnull robustness and optimality robustness of some tests for covariance structure including a test for sphericity. Second, we show the optimality robustness of the LBI tests in the GMANOVA(MANOVA) problem, and the problem of testing independence. In the GMANOVA problem, a robustness property of an essentially complete class of invariant tests is also shown.

Article information

Source
Ann. Statist., Volume 13, Number 3 (1985), 1182-1197.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349663

Digital Object Identifier
doi:10.1214/aos/1176349663

Mathematical Reviews number (MathSciNet)
MR803765

Zentralblatt MATH identifier
0586.62078

JSTOR
links.jstor.org

Subjects
Primary: 62E10: Characterization and structure theory
Secondary: 62H05: Characterization and structure theory

Keywords
Null and nonnull robustness optimality robustness GMANOVA problem LBI test invariance sphericity

Citation

Kariya, Takeaki; Sinha, Bimal Kumar. Nonnull and Optimality Robustness of Some Tests. Ann. Statist. 13 (1985), no. 3, 1182--1197. doi:10.1214/aos/1176349663. https://projecteuclid.org/euclid.aos/1176349663


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