Albers, C. J.; Critchley, F. and Gower, J. C.
|DOI (Digital Object Identifier) Link:||http://dx.doi.org/doi:10.1016/j.jmva.2010.11.009|
|Google Scholar:||Look up in Google Scholar|
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.|
|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
|Depositing User:||Frank Critchley|
|Date Deposited:||08 Jan 2011 11:31|
|Last Modified:||23 Oct 2012 14:24|
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