Nested error regression models are commonly used to incorporate observational unit specific auxiliary variables to improve small area estimates. When the mean structure of this model is misspecified, there is generally an increase in the mean square prediction error (MSPE) of Empirical Best Linear Unbiased Predictors (EBLUP). Observed Best Prediction (OBP) method has been proposed with the intent to improve on the MSPE over EBLUP. We conduct a Monte Carlo simulation experiment to understand the effect of mispsecification of mean structures on different small area estimators. Our simulation results lead to an unexpected result that OBP may perform very poorly when observational unit level auxiliary variables are used and that OBP can be improved significantly when population means of those auxiliary variables (area level auxiliary variables) are used in the nested error regression model or when a corresponding area level model is used. Our simulation also indicates that the MSPE of OBP in an increasing function of the difference between the sample and population means of the auxiliary variables.

翻译：嵌套误差回归模型通常用于整合观测单元特定辅助变量，以改进小区域估计。当该模型的均值结构被误设时，经验最佳线性无偏预测器（EBLUP）的均方预测误差（MSPE）通常会增大。观测最佳预测（OBP）方法旨在改善EBLUP的MSPE性能。我们通过蒙特卡罗模拟实验探究均值结构误设对不同小区域估计量的影响。模拟结果得出一项意外发现：当使用观测单元级辅助变量时，OBP的性能可能非常差；而若在嵌套误差回归模型中引入这些辅助变量的总体均值（即区域级辅助变量），或改用相应的区域级模型，OBP的性能可显著提升。模拟还表明，OBP的MSPE随着辅助变量样本均值与总体均值之差的增大而递增。