Sphericity test in a GMANOVA-MANOVA model with normal error

JOURNAL OF MULTIVARIATE ANALYSIS

卷:100

Article

Bai, Peng

关键词: GMANOVA-MANOVA model;    Sphericity test;    Null distribution;    Meijer's G(p,p)(p,0) function;    Asymptotic distribution;    Bartlett type correction;   

DOI  :  10.1016/j.jmva.2009.03.003

来源: Elsevier

【 摘 要 】

For the GMANOVA-MANOVA model with normal error: Y = XB(1)Z(1)' + B(2)Z(2)' + epsilon, epsilon similar to N-qxn(0, I-n circle times Sigma), we study in this paper the sphericity hypothesis test problem with respect to covariance matrix: Sigma = lambda I-q (lambda is unknown). It is shown that, as a function of the likelihood ratio statistic Lambda, the null distribution of Lambda(2/n) can be expressed by Meijer's G(p,q)(p,0) function, and the asymptotic null distribution of -2 log Lambda is chi(2)(q(q+1)//2-1) (as n -> infinity). In addition, the Bartlett type correction -2 rho log Lambda for log Lambda is indicated to be asymptotically distributed as chi(2)(q(q+1)/2-1) with order n(-2) for an appropriate Bartlett adjustment factor -2 rho under null hypothesis. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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