Monotonicity of the power functions of some tests of hypotheses concerning multivariate complex normal distributions

Pillai, K. C. S.; Li, Hung C.

doi:10.1007/bf02506346

Cited by 2 publications

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Pillai and Li [18] have extended to the complex case the results on the monotonicity of power proved in the real case by the authors Anderson and Das Gupta [2]; Das Gupta, Anderson and Mudholkar [3], Anderson and Das Gupta [1], and Mudholkar [14]. However these results relate only to the monotonicity of power and do not serve to compare the powers of the tests of any of the three hypotheses based on the four criteria.…”

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

confidence: 99%

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract