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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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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DOI: https://doi.org/10.1023/A:1003487030859