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May, 1975 Exact Robustness Studies of Tests of Two Multivariate Hypotheses Based on Four Criteria and Their Distribution Problems Under Violations
K. C. S. Pillai, Sudjana
Ann. Statist. 3(3): 617-636 (May, 1975). DOI: 10.1214/aos/1176343126

Abstract

This paper deals with robustness studies of tests of two hypotheses (A) $\Sigma_1 = \Sigma_2$ in $N(\mu_i, \Sigma_i), i = 1, 2$, and (B) $\mu_1 = \cdots = \mu_l$ in $N(\mu_i, \Sigma), i = 1, 2, \cdots, l, \Sigma$ unknown, based on four test criteria (a) Hotelling's trace, (b) Pillai's trace, (c) Wilks' $\Lambda$ and (d) Roy's largest root. The robustness for (A) is against non-normality and for (B) against unequal covariance matrices and is studied in the exact case, unlike the results obtained earlier. In this connection, Pillai's density of the latent roots of $\mathbb{S}_1\mathbb{S}_2^{-1}$ under violations is used to derive the distributions or the moments of the criteria. Numerical studies of the tests of the two hypotheses based on the four criteria are made for the two-roots case.

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K. C. S. Pillai. Sudjana. "Exact Robustness Studies of Tests of Two Multivariate Hypotheses Based on Four Criteria and Their Distribution Problems Under Violations." Ann. Statist. 3 (3) 617 - 636, May, 1975. https://doi.org/10.1214/aos/1176343126

Information

Published: May, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0342.62032
MathSciNet: MR378250
Digital Object Identifier: 10.1214/aos/1176343126

Subjects:
Primary: 62H10
Secondary: 62H15

Keywords: Distribution problems under violations , exact robustness , Hotelling's trace , non-normality , Pillai's trace , Roy's largest root , tabulations , tests of multivariate hypotheses , unequal covariance matrices , Wilks' criterion

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 3 • May, 1975
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