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A simple explanation for the non-invariance of a Wald statistic to a reformulation of a null hypothesis

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  • Naorayex K Dastoor

    () (Department of Economics, University of Alberta)

Abstract

For a given null hypothesis and its reformulation, the associated Wald statistics are shown to be members of a wider family of statistics where all members are asymptotically equivalent under the null hypothesis. Therefore, the non-invariance of a Wald statistic (to a reformulation of a null hypothesis) is equivalent to using different members of the wider family and, in addition, this non-invariance implies that these members use different estimators of an appropriate variance-covariance matrix.

Suggested Citation

  • Naorayex K Dastoor, 2008. "A simple explanation for the non-invariance of a Wald statistic to a reformulation of a null hypothesis," Economics Bulletin, AccessEcon, vol. 3(62), pages 1-10.
  • Handle: RePEc:ebl:ecbull:eb-08c10010
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    References listed on IDEAS

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    1. Critchley, Frank & Marriott, Paul & Salmon, Mark, 1996. "On the Differential Geometry of the Wald Test with Nonlinear Restrictions," Econometrica, Econometric Society, vol. 64(5), pages 1213-1222, September.
    2. Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-1083, September.
    3. Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, vol. 59(6), pages 1601-1615, November.
    4. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    5. Kemp, Gordon C. R., 2001. "Invariance and the Wald test," Journal of Econometrics, Elsevier, vol. 104(2), pages 209-217, September.
    6. Lafontaine, Francine & White, Kenneth J., 1986. "Obtaining any Wald statistic you want," Economics Letters, Elsevier, vol. 21(1), pages 35-40.
    7. Dastoor, Naorayex K., 2003. "The equality of comparable extended families of classical-type and Hausman-type statistics," Journal of Econometrics, Elsevier, vol. 117(2), pages 313-330, December.
    8. Gourieroux, C. & Monfort, A., 1989. "A General Framework for Testing a Null Hypothesis in a “Mixed” Form," Econometric Theory, Cambridge University Press, vol. 5(01), pages 63-82, April.
    9. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-1468, November.
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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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