This research will extend the foundational, theoretical, computational and diagnostic methods of parametric empirical Bayesian and hierarchical Bayesian techniques in statistics. The work will include estimators for exponential families, using generalized linear models for the parameters and developing interval estimates in a variety of settings, including complicated cases with unequal sample sizes. To facilitate better fitting of real data, diagnostic methods will be developed to investigate modeling assumptions for the family of distributions governing the parameter and likelihoood graphics for the hyperparameters. Construction will be aided by use of an empirical Bayes bootstrap and an approximation technique using Pearson families ("adjusted likelihood"). Empirical Bayesian and hierarchical Bayesian techniques will be extended to model and solve problems concerning censored data, spatial modeling, meta- analysis and ranking.
