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

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