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...

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...

Under appropriate conditions, some asymptotic test statistics based on generalized inverses (g-inverses) are shown to be arbitrary in the sense that any desired numerical value for a statistic can be obtained by appropriately choosing a g-inverse of an estimator. Examples of statistics based on...