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Quadratic minimisation problems in statistics

Albers, C.J.; Critchley, F. and Gower, J. C. (2011). Quadratic minimisation problems in statistics. Journal of Multivariate Analysis, 102(3) pp. 698–713.

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We consider the problem minx(x – t)’A(x – t) subject to x’Bx + 2b’x = k where A is positive definite or positive semi-definite. Variants of this problem are discussed within the framework of a general unifying methodology. These include non-trivial considerations that arise when (i) A and/or B are not of full rank and (ii) t takes special forms (especially t = 0 which, under further conditions, reduces to the well-known two-sided eigenvalue solution). Special emphasis is placed on insights provided by geometrical interpretations.

Item Type: Journal Item
Copyright Holders: 2010 Elsevier Inc.
ISSN: 0047-259X
Keywords: canonical analysis; constraints; geometry; minimisation; quadratic forms; ratios; reduced rank
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 26089
Depositing User: Frank Critchley
Date Deposited: 13 Jan 2011 12:05
Last Modified: 04 Oct 2016 10:54
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