Exact robustness studies of the test of independence based on four multivariate criteria and their distribution problems under violations |
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Authors: | K C S Pillai Yu-Sheng Hsu |
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Institution: | (1) Purdue University, West Lafayette, USA |
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Abstract: | Summary Exact robustness studies against non-normality have been carried out for test of independence based on the four multivariate
criteria: Hotelling's trace,U
(p)
, Pillai's trace,V
(p)
, Wilks' criterion,W
(p)
, and Roy's largest root,L
(p)
. The density functions ofU
(p)
,W
(p)
andL
(p)
have been obtained in the canonical correlation case and further the moments ofU
(p)
and m.g.f. ofV
(p)
have been derived. All of the study is based on Pillai's distribution of the characteristic roots under violations. Numerical
results for the power function have been tabulated for the two-roots case. Slight non-normality does not affect the independence
test seriously.V
(2) is found to be most robust against nonnormality.
Yu-Sheng Hsu is now with Georgia State University, Atlanta. |
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Keywords: | 62H10 62H15 |
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