This paper studies models in which hypothesis tests have trivial power, that is, power smaller than size. This testing impossibility, or impossibility type A, arises when any alternative is not distinguishable from the null. We also study settings where it is impossible to have almost surely...

This article compares two asymmetric Gaussian likelihood models and their corresponding estimators. Recently, there has been confusion in the literature regarding these models and: (1) whether they are the same, or (2) whether both of them can be used to estimate expectiles. After the...