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Zbl 0554.62055
Lin, Chun-tu
Extrema of quadratic forms and statistical applications.
(English)
[J] Commun. Stat., Theory Methods 13, 1517-1520 (1984). ISSN 0361-0926; ISSN 1532-415X/e

{\it C. G. Khatri} and {\it C. R. Rao} [J. Multivariate Anal. 11, 498-505 (1981; Zbl 0482.15010)] gave a bound to the ratio of the determinants $\vert X'B\sp 2X\vert \vert X'C\sp 2X\vert /\vert X'BCX\vert$, where X is an $n\times k$ matrix of rank k, and B, C are commutative matrices. In this paper, we provide bounds to the ratios of the determinants $\vert X'AX\vert /\vert X'X\vert$ and a more general result than that of Khatri and Rao. The results can be applied to some problems in statistics.
MSC 2000:
*62H99 Multivariate analysis
15A63 Bilinear forms, etc.

Keywords: extrema of quadratic forms; Kantorovich inequality; positive definite matrices; bounds; ratios of the determinants

Citations: Zbl 0482.15010

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