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2008 | 28 | 1 | 113-137
Tytuł artykułu

An alternative approach to characterize the commutativity of orthogonal projectors

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In an invited paper, Baksalary [Algebraic characterizations and statistical implications of the commutativity of orthogonal projectors. In: T. Pukkila, S. Puntanen (Eds.), Proceedings of the Second International Tampere Conference in Statistics, University of Tampere, Tampere, Finland, [2], pp. 113-142] presented 45 necessary and sufficient conditions for the commutativity of a pair of orthogonal projectors. Basing on these results, he discussed therein also statistical aspects of the commutativity with reference to problems concerned with canonical correlations and with comparisons between estimators and between sets of linearly sufficient statistics corresponding to different linear models. In the present paper, parts of this analysis are resumed in order to shed some additional light on the problem of commutativity. The approach utilized is different than the one used by Baksalary, and is based on representations of projectors in terms of partitioned matrices. The usefulness of such representations is demonstrated by reinvestigating some of Baksalary's statistical considerations.
  • Institute of Physics, Adam Mickiewicz University, Umultowska 85, PL 61-614 Poznań, Poland
  • Department of Statistics, Dortmund University of Technology, Vogelpothsweg 87, D-44221 Dortmund, Germany
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