  Shrinkage estimators have profound impacts in statistics and in scientific
and engineering applications. In this article, we consider shrinkage estimation
in the presence of linear predictors. We formulate two heteroscedastic
hierarchical regression models and study optimal shrinkage estimators in each
model. A class of shrinkage estimators, both parametric and semiparametric,
based on unbiased risk estimate (URE) is proposed and is shown to be
(asymptotically) optimal under mean squared error loss in each model.
Simulation study is conducted to compare the performance of the proposed
methods with existing shrinkage estimators. We also apply the method to real
data and obtain encouraging and interesting results.
