On the Structure of Transformation Models

Abstract

In this paper we characterize transformation models by means of the functional form of the densities. We discuss sufficiency of the pair $(t, \pi)$ where $t$ is an equivariant estimator and $\pi$ is a maximal invariant. Furthermore, we introduce and discuss the algebraic concept of structural sufficiency. This gives rise to an example of a transformation model where $(t, \pi)$ is nonsufficient.