Bayes-suggested solutions in binomial estimation

This dissertation is concerned with the estimation of three functions of the binomial probability of "success": estimation of a linear combination of independent binomial probabilities; fixed precision estimation of the binomial probability; and estimation of the logit transformation of the binomial probability. A Bayesian viewpoint is adopted temporarily to "suggest" a wide class of admissible estimators for each problem. Designated the class C of SBP estimators, it is the class of Bayes estimators derived from Symmetric Beta Priors (the class of conjugate priors for the binomial), and often includes the maximum likelihood estimator as a special case. Once a class of estimators for each problem is suggested by the Bayesian viewpoint, three criteria are used to obtain the "optimum" estimators in that class. Two of these criteria are classical in nature: minimax risk and minimax weighted risk. The third criterion, the solution of which is the estimator corresponding to the "least favorable" prior in the class of priors considered, is subjective in nature and would appeal more to Bayesians. For each of the three problems, a class C of SBP estimators is suggested, and the optimum estimators from this class are obtained. In addition, for a special case in the estimation of a linear combination of binomials, an estimator is found that is minimax among all estimators, as well as minimax among SBP 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

1971

Author dc:creator

• DeRouen, Timothy Allen

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/10919/91028

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/91028