On the structure of transformation models

In this paper we characterize transformation models by means of the functional form of the densities. We discuss sufficiency of the pair (t,π)(t,π) where tt is an equivariant estimator and ππ 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,π)(t,π) is nonsufficient.