Publisher's Synopsis
This research note deals with a structural theory of statistical experiments irrespective of the complexity of the underlying model. To avoid involved measure theoretic arguments, functional analytic means are employed, following LeCam's decision theoretic approach.;The book provides a self-contained and unified introduction to the concept of generalized random variables and also includes a new, systematic discussion of the multivariate and even infinite-dimensional case. After the concepts of loss functions, subfields, and conditional expectation in this context have been presented, emphasis is laid on sufficiency, invariance, as well as optimality and admissibility in unbiased estimation. An appendix is devoted to an alternative approach due to Torgersen.;Apart from original results, this work also contains new proofs and characterizations of facts occurring in the periodic literature only, faciliating access also to researchers outside the fields of this branch of statistical decision theory and/or advanced measure theory.
