IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v47y1982i2p187-199.html
   My bibliography  Save this article

Rank-reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis

Author

Listed:
  • Alexander Shapiro

Abstract

No abstract is available for this item.

Suggested Citation

  • Alexander Shapiro, 1982. "Rank-reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 187-199, June.
    • Handle: RePEc:spr:psycho:v:47:y:1982:i:2:p:187-199
    DOI: 10.1007/BF02296274
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/BF02296274
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/BF02296274?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Louis Guttman, 1958. "To what extent can communalities reduce rank?," Psychometrika, Springer;The Psychometric Society, vol. 23(4), pages 297-308, December.
    2. Giacomo Riccia & Alexander Shapiro, 1982. "Minimum rank and minimum trace of covariance matrices," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 443-448, December.
    3. Alexander Shapiro, 1982. "Weighted minimum trace factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(3), pages 243-264, September.
    4. Jos Berge & Tom Snijders & Frits Zegers, 1981. "Computational aspects of the greatest lower bound to the reliability and constrained minimum trace factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 46(2), pages 201-213, June.
    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. Bai, Jushan & Ng, Serena, 2019. "Rank regularized estimation of approximate factor models," Journal of Econometrics, Elsevier, vol. 212(1), pages 78-96.
    2. Shapiro, Alexander, 2009. "Asymptotic normality of test statistics under alternative hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 936-945, May.
    3. Knott, Martin, 2005. "A measure of independence for a multivariate normal distribution and some connections with factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 374-383, October.
    4. Peter Bentler, 2009. "Alpha, Dimension-Free, and Model-Based Internal Consistency Reliability," Psychometrika, Springer;The Psychometric Society, vol. 74(1), pages 137-143, March.
    5. Jos Berge & Gregor Sočan, 2004. "The greatest lower bound to the reliability of a test and the hypothesis of unidimensionality," Psychometrika, Springer;The Psychometric Society, vol. 69(4), pages 613-625, December.
    6. Alexander Shapiro & Jos Berge, 2000. "The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 413-425, September.
    7. Jos Berge & Henk Kiers, 1991. "A numerical approach to the approximate and the exact minimum rank of a covariance matrix," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 309-315, June.
    8. Tyler Hunt & Peter Bentler, 2015. "Quantile Lower Bounds to Reliability Based on Locally Optimal Splits," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 182-195, March.
    9. Alexander Shapiro, 1982. "Weighted minimum trace factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(3), pages 243-264, September.
    10. Yanjun Wang & Ruizhi Shi & Jianming Shi, 2015. "Duality and robust duality for special nonconvex homogeneous quadratic programming under certainty and uncertainty environment," Journal of Global Optimization, Springer, vol. 62(4), pages 643-659, August.
    11. Kaufmann, Sylvia & Schumacher, Christian, 2019. "Bayesian estimation of sparse dynamic factor models with order-independent and ex-post mode identification," Journal of Econometrics, Elsevier, vol. 210(1), pages 116-134.
    12. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    13. Defeng Sun, 2006. "The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 761-776, November.
    14. Jushan Bai & Serena Ng, 2017. "Principal Components and Regularized Estimation of Factor Models," Papers 1708.08137, arXiv.org, revised Nov 2017.

    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. Jos Berge & Henk Kiers, 1991. "A numerical approach to the approximate and the exact minimum rank of a covariance matrix," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 309-315, June.
    2. Knott, Martin, 2005. "A measure of independence for a multivariate normal distribution and some connections with factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 374-383, October.
    3. Paul Bekker & Jan Leeuw, 1987. "The rank of reduced dispersion matrices," Psychometrika, Springer;The Psychometric Society, vol. 52(1), pages 125-135, March.
    4. Armeen Taeb & Parikshit Shah & Venkat Chandrasekaran, 2020. "False discovery and its control in low rank estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(4), pages 997-1027, September.
    5. Peter M. Bentler, 2021. "Alpha, FACTT, and Beyond," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 861-868, December.
    6. Bai, Jushan & Ng, Serena, 2019. "Rank regularized estimation of approximate factor models," Journal of Econometrics, Elsevier, vol. 212(1), pages 78-96.
    7. Li Cui & Lu Liu & Di-Rong Chen & Jian-Feng Xie, 2016. "Recovery of Low Rank Symmetric Matrices via Schatten p Norm Minimization," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-11, February.
    8. Alexander Shapiro & Jos Berge, 2000. "The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 413-425, September.
    9. Tyler Hunt & Peter Bentler, 2015. "Quantile Lower Bounds to Reliability Based on Locally Optimal Splits," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 182-195, March.
    10. Lee Cronbach, 1988. "Internal consistency of tests: Analyses old and new," Psychometrika, Springer;The Psychometric Society, vol. 53(1), pages 63-70, March.
    11. Klaas Sijtsma, 2012. "Future of Psychometrics: Ask What Psychometrics Can Do for Psychology," Psychometrika, Springer;The Psychometric Society, vol. 77(1), pages 4-20, January.
    12. Jos Berge & Henk Kiers, 1999. "Retrieving the correlation matrix from a truncated PCA solution: The inverse principal component problem," Psychometrika, Springer;The Psychometric Society, vol. 64(3), pages 317-324, September.
    13. David J. Hessen, 2017. "Lower Bounds to the Reliabilities of Factor Score Estimators," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 648-659, September.
    14. Harold Bechtoldt, 1961. "An empirical study of the factor analysis stability hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 26(4), pages 405-432, December.
    15. Samuel Burer & Moshe Dror, 2012. "Newsvendor games: convex optimization of centralized inventory operations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 707-728, October.
    16. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    17. Jos Berge & Tom Snijders & Frits Zegers, 1981. "Computational aspects of the greatest lower bound to the reliability and constrained minimum trace factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 46(2), pages 201-213, June.
    18. M Dror & B C Hartman, 2011. "Survey of cooperative inventory games and extensions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 565-580, April.
    19. Jos Berge & Willem Hofstee, 1999. "Coefficients alpha and reliabilities of unrotated and rotated components," Psychometrika, Springer;The Psychometric Society, vol. 64(1), pages 83-90, March.
    20. Jushan Bai & Serena Ng, 2017. "Principal Components and Regularized Estimation of Factor Models," Papers 1708.08137, arXiv.org, revised Nov 2017.

    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:spr:psycho:v:47:y:1982:i:2:p:187-199. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.