Shrinkage Estimates in a Two-Level Heteroscedastic Hierarchical Normal Models With Linear Trend Mean

Abstract

In heteroscedastic hierarchical normal models, often, the response variable may rather fluctuate around a nonconstant trend than a constant value. In this paper, we assume a linear trend for the second level of a two-level heteroscedastic hierarchical normal model. The empirical Bayes maximum likelihood estimates, Stein's unbiased risk estimates, and Bayesian estimates of the hyperparameters are elicited and the corresponding shrinkage estimates are constructed. The asymptotic properties of the Stein's unbiased risk estimates are illustrated. Since our primary purpose in Bayesian analysis is sampling from the posterior distributions, with assuming some priors for the hyperparameters, the posterior full conditions are given. A real data set is analyzed to demonstrate the proposed methodology. i

Bayesian analysis of hierarchical heteroscedastic linear models using Dirichlet-Laplace priors

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