On the structure of transformation models (Q1825551)

In contrast to earlier work in which particular transformation models were studied, or which considered general treatments of transformation models in special cases, this paper is devoted to the introduction of a basic set-up for transformation models, in which set-up models are characterized by means of their densities. The concept of unique maximum likelihood estimation is discussed. The sufficiency of (t,\(\pi)\), where t is an equivariant estimator and \(\pi\) is a maximal invariant, is examined, and the algebraic concept of structural sufficiency is introduced. The author notes that ``readers not familiar with topology and the theory of invariant measures can read the paper disregarding the details and still be able to understand the main results''.