Sciweavers

Share
MA
2011
Springer

Quadratic minimisation problems in statistics

8 years 1 months ago
Quadratic minimisation problems in statistics
We consider the problem minx(x−t) A(x−t) subject to x Bx + 2b x = k where A is positive definite or positive semidefinite. Commonly occurring statistical 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. Algorithmic considerations are discussed and examples given. Keywords. canonical analysis, constraints, geometry, Hardy-Weinberg, minimisation, optimal scaling, Procrustes analysis, quadratic forms, ratios, reduced rank, splines. 1
Casper J. Albers, Frank Critchley, John C. Gower
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where MA
Authors Casper J. Albers, Frank Critchley, John C. Gower
Comments (0)
books