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Quadratic minimisation problems in statistics

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  • Albers, C.J.
  • Critchley, F.
  • Gower, J.C.

Abstract

We consider the problem subject to where 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) and/or are not of full rank and (ii) takes special forms (especially which, under further conditions, reduces to the well-known two-sided eigenvalue solution). Special emphasis is placed on insights provided by geometrical interpretations.

Suggested Citation

  • Albers, C.J. & Critchley, F. & Gower, J.C., 2011. "Quadratic minimisation problems in statistics," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 698-713, March.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:698-713
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    References listed on IDEAS

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    1. Roderick McDonald & Yukihiko Torii & Shizuhiko Nishisato, 1979. "Some results on proper eigenvalues and eigenvectors with applications to scaling," Psychometrika, Springer;The Psychometric Society, vol. 44(2), pages 211-227, June.
    2. Jan Leeuw, 1982. "Generalized eigenvalue problems with positive semi-definite matrices," Psychometrika, Springer;The Psychometric Society, vol. 47(1), pages 87-93, March.
    3. Henk Kiers, 1995. "Maximization of sums of quotients of quadratic forms and some generalizations," Psychometrika, Springer;The Psychometric Society, vol. 60(2), pages 221-245, June.
    4. Elliot Cramer, 1974. "On browne's solution for oblique procrustes rotation," Psychometrika, Springer;The Psychometric Society, vol. 39(2), pages 159-163, June.
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    Cited by:

    1. Albers, C.J. & Critchley, F. & Gower, J.C., 2011. "Applications of quadratic minimisation problems in statistics," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 714-722, March.
    2. Casper Albers & John Gower, 2014. "Canonical Analysis: Ranks, Ratios and Fits," Journal of Classification, Springer;The Classification Society, vol. 31(1), pages 2-27, April.
    3. Stefan Jakubek & Elisabeth Luchini & Alexander Oberhummer & Felix Pfister, 2016. "A model-based interfacing concept for accurate power hardware-in-the-loop systems," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 22(1), pages 1-20, January.

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