Degree Type

Dissertation

Date of Award

1982

Degree Name

Doctor of Philosophy

Department

Statistics

Abstract

The estimation of a parameter vector for multivariate distributions has been studied extensively in the classical, Bayesian, empirical Bayes, and James-Stein framework. Shrinkage estimation procedures of Thompson and Albert are extended to form new estimators of such parameter vectors. These estimators are given for the normal, Poisson and gamma setting and the consequences of varying the focus and flexibility of the shrinkers are studied. When possible, the resulting estimators are given an empirical Bayes interpretation;These estimators are also utilized in estimating the mean of a stratified normal population;Using the method of moments technique, an empirical Bayes estimator of a multivariate scale parameter vector is developed and studied;Also, multivariate estimators are proposed that improve upon the simultaneous estimation procedures of Brown and Shinozaki. The major tool is the use of integration by parts techniques in solving basic differential inequalities;When possible, the estimators are evaluated through simulation studies.

DOI

https://doi.org/10.31274/rtd-180813-7941

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Richard E. Auer

Language

en

Proquest ID

AAI8307733

File Format

application/pdf

File Size

196 pages

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