Jespersen, Niels Christian Bang On the structure of transformation models. (English) Zbl 0684.62009 Ann. Stat. 17, No. 1, 195-208 (1989). 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”. Reviewer: A.Dale Cited in 1 Document MSC: 62A01 Foundations and philosophical topics in statistics 62B05 Sufficient statistics and fields 57S99 Topological transformation groups Keywords:invariance; proper action; homogeneous space; transformation models; set- up models; unique maximum likelihood estimation; equivariant estimator; maximal invariant; structural sufficiency × Cite Format Result Cite Review PDF Full Text: DOI