A simple explanation for the non-invariance of a Wald statistic to a reformulation of a null hypothesis
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.
Volume (Year): 3 (2008)
Issue (Month): 62 ()
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"On the Formulation of Wald Tests of Nonlinear Restrictions,"
Cowles Foundation Discussion Papers
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