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

Author

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  • Jiménez Gamero, M.D.
  • Muñoz García, J.
  • Pino Mejías, R.

Abstract

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.

Suggested Citation

  • Jiménez Gamero, M.D. & Muñoz García, J. & Pino Mejías, R., 2005. "Testing goodness of fit for the distribution of errors in multivariate linear models," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 301-322, August.
  • Handle: RePEc:eee:jmvana:v:95:y:2005:i:2:p:301-322
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    References listed on IDEAS

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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. L. Baringhaus & N. Henze, 1988. "A consistent test for multivariate normality based on the empirical characteristic function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 35(1), pages 339-348, December.
    4. 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.
    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. 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.
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    Cited by:

    1. Meintanis, Simos G. & Ngatchou-Wandji, Joseph & Taufer, Emanuele, 2015. "Goodness-of-fit tests for multivariate stable distributions based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 171-192.
    2. V. Alba Fernández & D. Barrera Rosillo & M. Ibáñez Pérez & M. Jiménez Gamero, 2009. "A homogeneity test for bivariate random variables," Computational Statistics, Springer, vol. 24(3), pages 513-531, August.
    3. Heuchenne, Cédric & Van Keilegom, Ingrid, 2010. "Goodness-of-fit tests for the error distribution in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1942-1951, August.

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