Empirical Bayes Estimation in Cross-Classified Gaussian Models With Unbalanced Design

Loading...
Thumbnail Image
Degree type
Doctor of Philosophy (PhD)
Graduate group
Statistics
Discipline
Subject
Compound Decision
Cross-Classified Models
Decision Theory
Empirical Bayes
Heteroscedasticity
Shrinkage Estimation
Statistics and Probability
Funder
Grant number
License
Copyright date
2016-11-29T00:00:00-08:00
Distributor
Related resources
Contributor
Abstract

The James-Stein estimator and its Bayesian interpretation demonstrated the usefulness of empirical Bayes methods in facilitating competitive shrinkage estimators for multivariate problems consisting of nonrandom parameters. When transitioning from homoscedastic to heteroscedastic Gaussian data, empirical ``linear Bayes" estimators typically lose attractive properties such as minimaxity, and are usually justified mainly from Bayesian viewpoints. Nevertheless, by appealing to frequentist considerations, traditional empirical linear Bayes estimators can be modified to better accommodate the asymmetry in unequal variance cases. This work develops empirical Bayes estimators for cross-classified (factorial) data with unbalanced design that are asymptotically optimal within classes of shrinkage estimators, and in particular asymptotically dominate traditional parametric empirical Bayes estimators as well the usual (unbiased) estimator.

Advisor
Lawrence D. Brown
Date of degree
2015-01-01
Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Volume number
Issue number
Publisher
Publisher DOI
Journal Issue
Comments
Recommended citation