A test of the hypothesis of partial common principal components |
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Authors: | Franti?ek Rublík |
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Institution: | 1.Institute of Measurement Science,Bratislava,Slovakia |
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Abstract: | A test of the equality of the first h eigenvectors of covariance matrices of several populations is constructed without the assumption that the sampled distributions
are Gaussian. It is proved that the test statistic is asymptotically chi-square distributed. In this general setting, an explicit
formula for column space of the asymptotic covariance matrix of the sample eigenvectors is derived and the rank of this matrix
is computed. An essential assumption in deriving the asymptotic distribution of the presented test statistic is the existence
of the finite fourth moments and the simplicity of the h largest eigenvalues of population covariance matrices, which makes possible to use the formulas for derivatives of eigenvectors
of symmetric matrices. |
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Keywords: | |
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