IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v102y2011i3p714-722.html
   My bibliography  Save this article

Applications of quadratic minimisation problems in statistics

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00239-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Yoshio Takane & Forrest Young & Jan Leeuw, 1977. "Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 42(1), pages 7-67, March.
    3. Michael Browne, 1967. "On oblique procrustes rotation," Psychometrika, Springer;The Psychometric Society, vol. 32(2), pages 125-132, June.
    4. Jan Leeuw, 1982. "Generalized eigenvalue problems with positive semi-definite matrices," Psychometrika, Springer;The Psychometric Society, vol. 47(1), pages 87-93, March.
    5. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-1468, November.
    6. Casper Albers & John Gower, 2010. "A general approach to handling missing values in Procrustes analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(4), pages 223-237, December.
    7. W. J. Krzanowski & P. Jonathan & W. V. McCarthy & M. R. Thomas, 1995. "Discriminant Analysis with Singular Covariance Matrices: Methods and Applications to Spectroscopic Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(1), pages 101-115, March.
    8. 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.
    9. Lafontaine, Francine & White, Kenneth J., 1986. "Obtaining any Wald statistic you want," Economics Letters, Elsevier, vol. 21(1), pages 35-40.
    10. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jean-Marie Dufour & Alain Trognon & Purevdorj Tuvaandorj, 2017. "Invariant tests based on M -estimators, estimating functions, and the generalized method of moments," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 182-204, March.
    2. Naorayex K Dastoor, 2008. "A simple explanation for the non-invariance of a Wald statistic to a reformulation of a null hypothesis," Economics Bulletin, AccessEcon, vol. 3(62), pages 1-10.
    3. Dastoor, Naorayex, 2009. "The perceived framework of a classical statistic: Is the non-invariance of a Wald statistic much ado about null thing?," Working Papers 2009-25, University of Alberta, Department of Economics.
    4. repec:ebl:ecbull:v:3:y:2008:i:62:p:1-10 is not listed on IDEAS
    5. Goh, Kim-Leng & King, Maxwell L., 1996. "Modified Wald tests for non-linear restrictions: A cautionary tale," Economics Letters, Elsevier, vol. 53(2), pages 133-138, November.
    6. Kemp, Gordon C. R., 2001. "Invariance and the Wald test," Journal of Econometrics, Elsevier, vol. 104(2), pages 209-217, September.
    7. Brown, Kenneth & Cribari-Neto, Francisco, 1992. "On Hypothesis Testing: A Selective Look at the Lagrange Multiplier, Likelihood Ratio and Wald Tests," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 12(2), November.
    8. Francisco J. Goerlich Gisbert, 1992. "Un test alternativo de la hipótesis de sustitución intertemporal del trabajo," Investigaciones Economicas, Fundación SEPI, vol. 16(2), pages 259-280, May.
    9. Helen Popper, 1995. "Term premia comovement in German, Japanese, and U.S. domestic markets," Open Economies Review, Springer, vol. 6(1), pages 49-62, January.
    10. Alessandra Canepa & Raymond O'Brien, 2000. "The Size and Power of Bootstrap Tests for Linear Restrictions in Misspecified Cointegrating Relationships," Econometric Society World Congress 2000 Contributed Papers 1807, Econometric Society.
    11. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, University Library of Munich, Germany, revised 05 Mar 1996.
    12. Paul Hansen, 1997. "Inference on “earnings dynamics over the life cycle: New evidence for New Zealand”," New Zealand Economic Papers, Taylor & Francis Journals, vol. 31(2), pages 221-227.
    13. Crudu, Federico & Osorio, Felipe, 2020. "Bilinear form test statistics for extremum estimation," Economics Letters, Elsevier, vol. 187(C).
    14. Lu, Zeng-Hua & King, Maxwell L., 2004. "A Wald-type test of quadratic parametric restrictions," Economics Letters, Elsevier, vol. 83(3), pages 359-364, June.
    15. Alexander, W. Robert J. & Hansen, Paul & Owen, P. Dorian, 1996. "Inference on productivity differentials in multi-sector models of economic growth," Journal of Development Economics, Elsevier, vol. 51(2), pages 315-325, December.
    16. Lung-fei Lee & Jihai Yu, 2012. "The C(α)-type gradient test for spatial dependence in spatial autoregressive models," Letters in Spatial and Resource Sciences, Springer, vol. 5(3), pages 119-135, October.
    17. Patrick Kline & Christopher R. Walters, 2016. "Evaluating Public Programs with Close Substitutes: The Case of HeadStart," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1795-1848.
    18. 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.
    19. Zaka Ratsimalahelo, 2017. "Generalised Wald type Test of nonlinear restrictions," Working Papers 2017-13, CRESE.
    20. Marcel G. Dagenais, 1992. "Pièges et limitations de l'analyse micro-économétrique," Économie et Prévision, Programme National Persée, vol. 102(1), pages 1-9.
    21. King, Maxwell L. & Zhang, Xibin & Akram, Muhammad, 2020. "Hypothesis testing based on a vector of statistics," Journal of Econometrics, Elsevier, vol. 219(2), pages 425-455.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:714-722. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.