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A test of the hypothesis of partial common principal components

In: Mathematica Slovaca, vol. 59, no. 5
František Rublík
Detaily:
Rok, strany: 2009, 579 - 592
Kľúčové slová:
asymptotic distribution of eigenvectors, rank of asymptotic covariance matrix, equality of eigenvectors of several populations
O článku:
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.
Ako citovať:
ISO 690:
Rublík, F. 2009. A test of the hypothesis of partial common principal components. In Mathematica Slovaca, vol. 59, no.5, pp. 579-592. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0149-9

APA:
Rublík, F. (2009). A test of the hypothesis of partial common principal components. Mathematica Slovaca, 59(5), 579-592. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0149-9
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