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Testing goodness of fit for the distribution of errors in multivariate linear models

  • Jiménez Gamero, M.D.
  • Muñoz García, J.
  • Pino Mejías, R.
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    In this paper, to test goodness of fit to any fixed distribution of errors in multivariate linear models, we consider a weighted integral of the squared modulus of the difference between the empirical characteristic function of the residuals and the characteristic function under the null hypothesis. We study the limiting behaviour of this test statistic under the null hypothesis and under alternatives. In the asymptotics, the rank of the design matrix is allowed to grow with the sample size.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 95 (2005)
    Issue (Month): 2 (August)
    Pages: 301-322

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    Handle: RePEc:eee:jmvana:v:95:y:2005:i:2:p:301-322
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    1. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(02), pages 316-356, June.
    2. Welsh, A. H., 1984. "A note on scale estimates based on the empirical characteristic function and their application to test for normality," Statistics & Probability Letters, Elsevier, vol. 2(6), pages 345-348, December.
    3. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
    4. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
    5. Epps, T. W., 1999. "Limiting behavior of the ICF test for normality under Gram-Charlier alternatives," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 175-184, April.
    6. Fan, Yanqin, 1998. "Goodness-Of-Fit Tests Based On Kernel Density Estimators With Fixed Smoothing Parameters," Econometric Theory, Cambridge University Press, vol. 14(05), pages 604-621, October.
    7. L. Baringhaus & N. Henze, 1988. "A consistent test for multivariate normality based on the empirical characteristic function," Metrika, Springer, vol. 35(1), pages 339-348, December.
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