Constrained Empirical Bayes Estimation in Multiplicative Area-Level Models with Risk Analysis Under an Asymmetric Loss Function



Mohammad Jafari Jozani (University of Manitoba, MB, Canada) (Speaker)
Elaheh Torkashvand (University of Waterloo, Canada)

Consider the problem of benchmarking small area estimates under multiplicative models with positive parameters where estimates are constrained to aggregate to direct estimates for the larger geographical areas. Constrained (hierarchical) empirical Bayes estimators of positive small area parameters under the conventional squared error loss function can take negative values. In this paper, we propose a loss function that guarantees positive estimates for small area parameters under multiplicative models. The hierarchical and constrained hierarchical empirical Bayes estimates of small area means and their corresponding risk functions under the new loss function are obtained. Also, the asymptotic and second-order unbiased risk estimators are provided. We implement the Jackknife method in order to reduce the bias of risk estimators. Finally, the performance of the proposed methods is investigated using simulation studies as well as a real data application.