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The Decomposition of the Behrens-Fisher Statistic in q-Dimensional Common Principal Component Submodels

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Abstract

Takemura (1985, Multivariate Analysis VI, ed. P. R. Krishnaiah, 583-597, Elsevier, Amsterdam) presented a decomposition of Hotelling's T2-statistic into analogues of univariate Student-t variates along the principal component axes of the (pooled) sample covariance matrix. In this paper the idea is extended to the heteroscedastic situation where an analogous decomposition of the Behrens-Fisher statistic is considered when the nature of the heteroscedasticity between the two samples can be described by a common principal component (CPC) model, or more particularly a q-dimensional CPC subspace model.

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Authors and Affiliations

  1. Department of Mathematical Statistics, University of the OFS, P.O, Box 339, Bloemfontein, 9300, South Africa

    D.G. Nel

  2. Department of Statistics, Vista University, Bloemfontein, 9300, South Africa

    I. Pienaar

Authors
  1. D.G. Nel
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  2. I. Pienaar
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Nel, D., Pienaar, I. The Decomposition of the Behrens-Fisher Statistic in q-Dimensional Common Principal Component Submodels. Annals of the Institute of Statistical Mathematics 50, 241–252 (1998). https://doi.org/10.1023/A:1003487030859

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