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Applications of quadratic minimisation problems in statistics

Albers, C. J.; Critchley, F. and Gower, J. C. (2011). Applications of quadratic minimisation problems in statistics. Journal of Multivariate Analysis, 102(3) pp. 714–722.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1016/j.jmva.2010.11.009
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Abstract

Albers et al. (2010) showed that the problem minx(x-t)'A(x-t) subject to x'Bx+2b'x=k where A is positive definite or positive semi-definite has a unique computable solution. Here, several statistical applications of this problem are shown to generate special cases of the general problem that may all be handled within a general unifying methodology. These include non-trivial considerations that arise when (i) A and/or B are not of full rank and (ii) where B is indefinite. General canonical forms for A and B that underpin the minimisation methodology give insight into structure that informs understanding.

Item Type: Journal Article
Copyright Holders: 2010 Elsevier Inc.
ISSN: 0047-259X
Keywords: Canonical analysis; Constraints; Constrained regression; Hardy–Weinberg; Minimisation; Optimal scaling; Procrustes analysis; Quadratic forms; Ratios; Reduced rank; Splines
Academic Unit/Department: Mathematics, Computing and Technology
Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 26088
Depositing User: Frank Critchley
Date Deposited: 08 Jan 2011 11:31
Last Modified: 23 Oct 2012 14:24
URI: http://oro.open.ac.uk/id/eprint/26088
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