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Applications of quadratic minimisation problems in statistics

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

Abstract

Albers et al. (2010) [2] showed that the problem subject to where 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) and/or are not of full rank and (ii) where is indefinite. General canonical forms for and that underpin the minimisation methodology give insight into structure that informs understanding.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:714-722
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    References listed on IDEAS

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    1. Critchley, Frank & Marriott, Paul & Salmon, Mark, 1996. "On the Differential Geometry of the Wald Test with Nonlinear Restrictions," Econometrica, Econometric Society, vol. 64(5), pages 1213-1222, September.
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    1. 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.
    2. 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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