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

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  • Alexander Shapiro

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  • 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
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    References listed on IDEAS

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    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

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    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Jushan Bai & Serena Ng, 2017. "Principal Components and Regularized Estimation of Factor Models," Papers 1708.08137, arXiv.org, revised Nov 2017.
    9. 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.
    10. Peter Bentler, 2009. "Alpha, Dimension-Free, and Model-Based Internal Consistency Reliability," Psychometrika, Springer;The Psychometric Society, vol. 74(1), pages 137-143, March.
    11. Alexander Shapiro, 1982. "Weighted minimum trace factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(3), pages 243-264, September.
    12. 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.
    13. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    14. 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.

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