Date of Award
Doctor of Philosophy
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.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Richard E. Auer
Auer, Richard E., "Shrinkage estimators for multiple parameters " (1982). Retrospective Theses and Dissertations. 8330.