The optimal extended balanced loss function estimators

We derive the optimal heterogeneous, homogeneous and homogeneous unbiased estimators of the coefficient vector in a linear regression model under the extended balanced loss function of Shalabh et al. (2009). Risk functions and optimal predictors of the new estimators are evaluated and comparisons among the estimators are made with respect to the extended balanced loss function. Some of the theoretical results are illustrated by a numerical example. Moreover, the behavior of the proposed estimators is studied via a Monte-Carlo experiment in the sense of mean square error.