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Asymptotic robustness in multi-sample analysis of multivariate linear relations

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Abstract

Standard methods for the analysis of linear latent variable models often rely on the assumption that the vector of observed variables is normally distributed. This normality assumption (NA) plays a crucial role in assessing optimality of estimates, in computing standard errors, and in designing an asymptotic chi-square goodness-of-fit test. The asymptotic validity of NA inferences when the data deviates from normality has been called asymptotic robustness. In the present paper we extend previous work on asymptotic robustness to a general context of multi-sample analysis of linear latent variable models, with a latent component of the model allowed to be fixed across (hypothetical) sample replications, and with the asymptotic covariance matrix of the sample moments not necessarily finite. We will show that, under certain conditions, the matrix $\Gamma$ of asymptotic variances of the analyzed sample moments can be substituted by a matrix $\Omega$ that is a function only of the cross- product moments of the observed variables. The main advantage of this is that inferences based on $\Omega$ are readily available in standard software for covariance structure analysis, and do not require to compute sample fourth-order moments. An illustration with simulated data in the context of regression with errors in variables will be presented.

Suggested Citation

  • Albert Satorra, 1995. "Asymptotic robustness in multi-sample analysis of multivariate linear relations," Economics Working Papers 126, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:126
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    1. Meissner, Joern & Strauss, Arne, 2012. "Network revenue management with inventory-sensitive bid prices and customer choice," European Journal of Operational Research, Elsevier, vol. 216(2), pages 459-468.
    2. Qian Liu & Garrett van Ryzin, 2008. "On the Choice-Based Linear Programming Model for Network Revenue Management," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 288-310, October.
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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