Year: 1998
Type: report
Abstract: Let a transformation group act on a sample space and induce a homomorphic group acting on the parameter space in the natural way.Both groups may be transitive or nontransitive and may have nontrivial stability groups; i.e., the orbits are not necessarily exact.An important class of parametric functionsthe invariantly estimable parameters -is introduced, and Bayes estimation with a right Haar measure of the group as a prior is shown to avoid inconsistencies (of the type described by Dawid, Stone and Zidak) when the group is fixed and when inference is confined to this class.Credibility sets (under Haar prior) and confidence sets are shown to be equal when generated by invariantly estimable parameters.Optimal equivariant estimators under the group are derived and shown to equal Bayes estimators under Haar prior.When the stability group has nonzero measure, modified results are proved using the theory of cocycles.The effect of different choices oftransformation group is illustrated by examples.
Author: Inge S. Helland
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2615543392