The Hypothesis of Multisample Block Sphericity

The p × p real matrix Σ is called block-spherical if it is diagonal with q blocks, 1 ≤ q ≤ p each containing$p_{i}$elements equal to$\sigma _{i}^{2},\,i=1,..,q,p_{1}+p_{2}+..+p_{q}=p$. The hypothesis of multisample block-sphericity is that k covariance matrices$\boldsymbol{\Sigma}_{j}$of p-variate n...

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Bibliographic Details
Published in:Sankhya. Series A 1992-06, Vol.54 (2), p.260-270
Main Author: Moschopoulos, Panagis G.
Format: Article
Language:English
Subjects:
Covariance matrices
Degrees of freedom
Mathematical functions
Mathematical moments
Mathematical theorems
Maximum likelihood estimators
Null hypothesis
Ratios
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Summary:The p × p real matrix Σ is called block-spherical if it is diagonal with q blocks, 1 ≤ q ≤ p each containing$p_{i}$elements equal to$\sigma _{i}^{2},\,i=1,..,q,p_{1}+p_{2}+..+p_{q}=p$. The hypothesis of multisample block-sphericity is that k covariance matrices$\boldsymbol{\Sigma}_{j}$of p-variate normal populations are block-spherical and equal. This paper considers the modified likelihood ratio test for multisample block-sphericity, its moments, and representations for its null and non-null distribution. In particular, it gives a series expansion for the non-null distribution under local alternatives. The paper extends the results in Moschopoulos (1988).
ISSN:0581-572X