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Symmetry, 0-1 Matrices, And Jacobians: A Review

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  • Magnus, J
  • Neudecker, H

Abstract

The purpose of the paper is to bring together those properties of the (simple) Kronecker product, the vec operator, and 0-1 matrices (commutation matrix, duplication matrix) that are thought to be of interest to researchers and students in econometrics and statistics. The treatment of Kronecker products and vec operators is fairly exhaustive; the treatment of 0-1 matrices is (deliberately) selective.

Suggested Citation

  • Magnus, J & Neudecker, H, 1985. "Symmetry, 0-1 Matrices, And Jacobians: A Review," University of Amsterdam, Actuarial Science and Econometrics Archive 293083, University of Amsterdam, Faculty of Economics and Business.
    • Handle: RePEc:ags:amstas:293083
    DOI: 10.22004/ag.econ.293083
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    Cited by:

    1. Turkington, Darrell A., 1998. "Efficient estimation in the linear simultaneous equations model with vector autoregressive disturbances," Journal of Econometrics, Elsevier, vol. 85(1), pages 51-74, July.
    2. Albert Satorra, 1990. "Robustness issues in structural equation modeling: a review of recent developments," Quality & Quantity: International Journal of Methodology, Springer, vol. 24(4), pages 367-386, November.
    3. Eduardo Abi Jaber & Bruno Bouchard & Camille Illand & Eduardo Jaber, 2018. "Stochastic invariance of closed sets with non-Lipschitz coefficients," Working Papers hal-01349639, HAL.
    4. Deaton, Angus, 1988. "Household Behavior in Developing Countries," Center Discussion Papers 321313, Yale University, Economic Growth Center.
    5. Hafner, C. M. & Linton, O., 2016. "Estimation of a Multiplicative Covariance Structure in the Large Dimensional Case," Cambridge Working Papers in Economics 1664, Faculty of Economics, University of Cambridge.
    6. Hafner, Christian M. & Linton, Oliver B. & Tang, Haihan, 2020. "Estimation of a multiplicative correlation structure in the large dimensional case," Journal of Econometrics, Elsevier, vol. 217(2), pages 431-470.
    7. Stavrev, Emil & Kambourov, Gueorgui, 1999. "Share Equations versus Double Logarithmic Functions in the Estimation of Income, Own- and Cross-Price Elasticities," Transition Economics Series 7, Institute for Advanced Studies.
    8. Martha Misas Arango & Enrique López Enciso & Juana Téllez Corredor & José Fernando Escobar, 2005. "La Inflación Subyacente en Colombia: Un Enfoque de Tendencias Estocásticas Comunes Asociadas a un VEC Estructural," Borradores de Economia 324, Banco de la Republica de Colombia.
    9. Reinaldo B. Arellano-Valle & Adelchi Azzalini, 2022. "Some properties of the unified skew-normal distribution," Statistical Papers, Springer, vol. 63(2), pages 461-487, April.
    10. Christian M. Hafner & Oliver Linton & Haihan Tang, 2016. "Estimation of a Multiplicative Covariance Structure," CeMMAP working papers CWP23/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Abi Jaber, Eduardo & Bouchard, Bruno & Illand, Camille, 2019. "Stochastic invariance of closed sets with non-Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1726-1748.
    12. Filipiak, Katarzyna & Klein, Daniel & Mokrzycka, Monika, 2024. "Discrepancy between structured matrices in the power analysis of a separability test," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    13. Katarzyna Filipiak & Daniel Klein & Anuradha Roy, 2015. "Score test for a separable covariance structure with the first component as compound symmetric correlation matrix," Working Papers 0148mss, College of Business, University of Texas at San Antonio.
    14. D.A. Turkington, 1997. "Some results in matrix calculus and an example of their application to econometrics," Economics Discussion / Working Papers 97-07, The University of Western Australia, Department of Economics.
    15. Filipiak, Katarzyna & Klein, Daniel & Roy, Anuradha, 2016. "Score test for a separable covariance structure with the first component as compound symmetric correlation matrix," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 105-124.
    16. Shaobo Jin & Sebastian Ankargren, 2019. "Frequentist Model Averaging in Structural Equation Modelling," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 84-104, March.
    17. Eduardo Abi Jaber & Bruno Bouchard & Camille Illand & Eduardo Abi Jaber, 2018. "Stochastic invariance of closed sets with non-Lipschitz coefficients," Post-Print hal-01349639, HAL.
    18. Stavrev, Emil & Kambourov, Gueorgui, 1999. "Estimation of Income, Own- and Cross-Price Elasticities. An Application for Bulgaria," Transition Economics Series 6, Institute for Advanced Studies.
    19. Christian M. Hafner & Oliver Linton & Haihan Tang, 2016. "Estimation of a Multiplicative Covariance Structure," CeMMAP working papers 23/16, Institute for Fiscal Studies.
    20. Linton, O. & Tang, H., 2020. "Estimation of the Kronecker Covariance Model by Quadratic Form," Cambridge Working Papers in Economics 2050, Faculty of Economics, University of Cambridge.
    21. Maddalena Cavicchioli, 2016. "Weak VARMA representations of regime-switching state-space models," Statistical Papers, Springer, vol. 57(3), pages 705-720, September.
    22. Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    23. Christian M. Hafner & Oliver Linton & Haihan Tang, 2016. "Estimation of a multiplicative covariance structure in the large dimensional case," CeMMAP working papers 52/16, Institute for Fiscal Studies.

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