Lower bounds for the variance of uniformly minimum variance unbiased estimators

The object of this paper was to study lower bounds ·for the variance of uniformly minimum variance unbiased estimators. The lower bounds of Cramer and Rao, Bhattacharyya, Hammersley, Chapman and Robbins, and Kiefer were derived and discussed. Each was compared with the other, showing their relative merits and shortcomings. Of the lower bounds considered all are greater than or equal to the Cramer-Rao lower bound. The Kiefer lower bound is as good as any of the others, or better. We were able to show that the Cramer-Rao lower bound is exactly the first Bhattacharyya lower bound. The Hammersley and the Chapman and Robbins lower bounds are identical when they both have the same parameter space, i.e., when Ω = (a,b). The use of the various lower bounds is illustrated in examples throughout the paper.

Name thesis:degree_name

M.S.

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Polytechnic Institute

Year dc:date.issued

1965

Author dc:creator

• Lemon, Glen Hortin

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/10919/104281

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/104281