Equivariant estimators and a special group structure

Given a G-invariant family of distributions and under suitable hypotheses concerning G, we characterize the form of G-equivariant estimators. In fact, corresponding to each G-equivariant estimator is an appropriate G-invariant function and conversely. In the course of characterizing the G-equivariant estimators, we obtain two maximal invariant functions. Some properties of these functions are obtained and in particular we calculate their densities with respect to an appropriate Haar measure. Finally, we consider an invariant estimator problem, the problem of estimating the orbit of a parameter. It is seen that this invariant problem may be referred back to an equivariant one. A loss function for the invariant problem is defined in such a way that the minimumr risk invariant estimator corresponds to the minimumr risk equivariant estimator within a subclass of all equivariant estimators.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1974

Author dc:creator

• Woteki, Thomas H.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10919/105397

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/105397