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Philip Byrne 《统计学通讯:理论与方法》2013,42(6):1935-1943
When a covariance matrix has a pattern associated with a stationary time series on the errors, it is shown how certain hypothesis testing problems In multivariate analysis can be transformed into a product of two similar multivariate problems that each involve unpatterned covariance matrices. 相似文献
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Consider the canonical-form MANOVA setup with X: n × p = (+ E, Xi ni × p, i = 1, 2, 3, Mi: ni × p, i = 1, 2, n1 + n2 + n3) p, where E is a normally distributed error matrix with mean zero and dispersion In (> 0 (positive definite). Assume (in contrast with the usual case) that M1i is normal with mean zero and dispersion In1) and M22 is either fixed or random normal with mean zero and different dispersion matrix In2 (being unknown. It is also assumed that M1 E, and M2 (if random) are all independent. For testing H0) = 0 versus H1: (> 0, it is shown that when either n2 = 0 or M2 is fixed if n2 > 0, the trace test of Pillai (1955) is uniformly most powerful invariant (UMPI) if min(n1, p)= 1 and locally best invariant (LBI) if min(n1 p) > 1 underthe action of the full linear group Gl (p). When p > 1, the LBI test is also derived under a somewhat smaller group GT(p) of p × p lower triangular matrices with positive diagonal elements. However, such results do not hold if n2 > 0 and M2 is random. The null, nonnull, and optimality robustness of Pillai's trace test under Gl(p) for suitable deviations from normality is pointed out. 相似文献
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