Statistical inference under symmetry

@inproceedings{Helland2003StatisticalIU,
  title={Statistical inference under symmetry},
  author={Inge S. Helland},
  year={2003}
}
We explore the consequences of adjoining a symmetry group to a statistical model. Group actions are first induced on the sample space, and then on the parameter space. It is argued that the right invariant measure induced by the group on the parameter space is a natural non-informative prior for the parameters of the model. The permissible sub-parameters are introduced, i.e., the subparameters upon which group actions can be defined. Equivariant estimators are similarly defined. Orbits of the… CONTINUE READING