Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]