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On the Asymptotic Optimality of Alternative Minimum-Distance Estimators in Linear Latent-Variable Models

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  • Satorra, Albert
  • Neudecker, Heinz

Abstract

In the context of linear latent-variable models, and a general type of distribution of the data, the asymptotic optimality of a subvector of minimum-distance estimators whose weight matrix uses only second-order moments is investigated. The asymptotic optimality extends to the whole vector of parameter estimators, if additional restrictions on the third-order moments of the variables are imposed. Results related to the optimality of normal (pseudo) maximum likelihood methods are also encompassed. The results derived concern a wide class of latent-variable models and estimation methods used routinely in software for the analysis of latent-variable models such as LISREL, EQS, and CALIS. The general results are specialized to the context of multivariate regression and simultaneous equations with errors in variables.

Suggested Citation

  • Satorra, Albert & Neudecker, Heinz, 1994. "On the Asymptotic Optimality of Alternative Minimum-Distance Estimators in Linear Latent-Variable Models," Econometric Theory, Cambridge University Press, vol. 10(5), pages 867-883, December.
    • Handle: RePEc:cup:etheor:v:10:y:1994:i:05:p:867-883_00
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    References listed on IDEAS

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    1. Anderson, T. W., 1989. "Linear latent variable models and covariance structures," Journal of Econometrics, Elsevier, vol. 41(1), pages 91-119, May.
    2. A. Mooijaart & P.M. Bentler, 1991. "Robustness of normal theory statistics in structural equation models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 45(2), pages 159-171, June.
    3. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
    4. Bentler, P. M., 1983. "Simultaneous equation systems as moment structure models : With an introduction to latent variable models," Journal of Econometrics, Elsevier, vol. 22(1-2), pages 13-42.
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    Cited by:

    1. M. Antònia Monés & Eva Ventura, 1993. "Saving decisions and fiscal incentives: A Spanish panel based analysis," Economics Working Papers 41, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Prokhorov, Artem, 2009. "On relative efficiency of quasi-MLE and GMM estimators of covariance structure models," Economics Letters, Elsevier, vol. 102(1), pages 4-6, January.
    3. Damba Lkhagvasuren, 2009. "Large Locational Differences in Unemployment Despite High Labor Mobility: Impact of Moving Cost on Aggregate Unemployment and Welfare," Working Papers 09009, Concordia University, Department of Economics, revised Mar 2010.
    4. Eva Ventura & Albert Satorra, 1998. "Lyfe-cycle effects on household expenditures: A latent-variable approach," Economics Working Papers 354, Department of Economics and Business, Universitat Pompeu Fabra.
    5. Ogasawara, Haruhiko, 2005. "Asymptotic robustness of the asymptotic biases in structural equation modeling," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 771-783, June.
    6. Prokhorov, Artem, 2012. "Second order bias of quasi-MLE for covariance structure models," Economics Letters, Elsevier, vol. 114(2), pages 195-197.
    7. Yuan, Ke-Hai & Bentler, Peter M., 1997. "Improving parameter tests in covariance structure analysis," Computational Statistics & Data Analysis, Elsevier, vol. 26(2), pages 177-198, December.
    8. Hayakawa, Kazuhiko, 2024. "Recent development of covariance structure analysis in economics," Econometrics and Statistics, Elsevier, vol. 29(C), pages 31-48.
    9. Yuan, Ke-Hai & Bentler, Peter M., 2005. "Asymptotic robustness of the normal theory likelihood ratio statistic for two-level covariance structure models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 328-343, June.

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