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
Copyright Date
1982
Language
en
Proquest ID
AAI8307733
File Format
application/pdf
File Size
196 pages
Recommended Citation
Auer, Richard E., "Shrinkage estimators for multiple parameters " (1982). Retrospective Theses and Dissertations. 8330.
https://lib.dr.iastate.edu/rtd/8330
