On a Property of a Test for the Equality of Two Normal Dispersion Matrices Against One-sided Alternatives

Mikhail, Wadie F.

doi:10.1214/aoms/1177704380

Cited by 5 publications

(1 citation statement)

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“…The monotonicity of the power function of L(~) has been demonstrated earlier by Roy and Mikhail [13], [23]. More recently Perlman [15] has shown that the power functions of the tests of 2) and 3) based on V (~) are monotonically increasing in each noncentrality parameter provided that the cut off point is not too large.…”

Section: Pr [Lc)~/} =D[(1-p~)(1-p~)] ~ ~ E ~ E B(r S)_f)~(l)mentioning

confidence: 67%

The distribution of the characteristic roots ofS 1 S 2 −1 under violations in the complex case and power comparisons of four tests

Pillai¹,

Hsu²

1979

Ann Inst Stat Math

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SummaryThe joint density function of the latent roots of S1S? ~ under violations is obtained where S~ has a complex non-central Wishart distribution We (p, n~, 2,~, [J) and $2, an independent complex central Wishart, Wo(p, n2, Z2, 0). The density and moments of Hotelling's trace are also derived under violations. Further, the non-null distributions of the following four criteria in the two-roots case are studied for tests of three hypotheses: Hotelling's trace, Pillai's trace, Wilks' criterion and Roy's largest root. In addition, tabulations of powers are carried out and power comparisons for tests of each of three hypotheses based on the four criteria are made in the complex case extending such work of Pillai and Jayachandran in the classical Gaussian case. The findings in the complex Gaussian are generally similar to those in the classical.

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Section: Pr [Lc)~/} =D[(1-p~)(1-p~)] ~ ~ E ~ E B(r S)_f)~(l)mentioning

confidence: 67%