Locally most powerful invariant tests for two dimensional alternatives (Q580853)

The purpose of this paper is to give an extension of locally most powerful scale and/or location invariant (LMPI) tests for \(H_ 0: \theta =\theta_ 0\) when \(\theta\) is a two dimensional shape parameter ranging over an open set \(\Theta \subseteq {\mathbb{R}}^ 2\) and \(\theta_ 0\) corresponds to a point of interest belonging to \(\Theta\). This approach can be of interest when a problem of check of distributional shape is faced embedding the model of interest and the alternative models in a single parametric family depending on two (or more) shape parameters. As an application, an approximate LMPI test of exponentiality against generalized gamma alternatives is obtained.