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Extrema of quadratic forms and statistical applications. (English) Zbl 0554.62055
C. G. Khatri and C. R. Rao [J. Multivariate Anal. 11, 498-505 (1981; Zbl 0482.15010)] gave a bound to the ratio of the determinants |X ' B 2 X||X ' C 2 X|/|X ' BCX|, where X is an n×k matrix of rank k, and B, C are commutative matrices. In this paper, we provide bounds to the ratios of the determinants |X ' AX|/|X ' X| and a more general result than that of Khatri and Rao. The results can be applied to some problems in statistics.
MSC:
62H99Multivariate analysis
15A63Quadratic and bilinear forms, inner products