Some complex variable transformations and exact power comparisons of two-sided tests of equality of two Hermitian covariance matrices |
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Authors: | SSylvia Chu KCS Pillai |
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Institution: | Purdue University, Lafayette, IN, USA |
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Abstract: | Power studies of tests of equality of covariance matrices of two p-variate complex normal populations σ1 = σ2 against two-sided alternatives have been made based on the following five criteria: (1) Roy's largest root, (2) Hotelling's trace, (4) Wilks' criterion and (5) Roy's largest and smallest roots. Some theorems on transformations and Jacobians in the two-sample complex Gaussian case have been proved in order to obtain a general theorem for establishing the local unbiasedness conditions connecting the two critical values for tests (1)–(5). Extensive unbiased power tabulations have been made for p=2, for various values of n1, n2, λ1 and λ2 where n1 is the df of the SP matrix from the ith sample and λ1 is the ith latent root of σ1σ-12 (i=1, 2). Equal tail areas approach has also been used further to compute powers of tests (1)–(4) for p=2 for studying the bias and facilitating comparisons with powers in the unbiased case. The inferences have been found similar to those in the real case. (Chu and Pillai, Ann. Inst. Statist. Math. 31. |
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Keywords: | 62M10 62M15 Jacobians Unbiased Roy's Largest Root Hotelling's Trace Pillai's Trace Wilks' Criterion Roy's Largest-Smallest Roots |
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