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：嵌套误差回归模型常用于结合观测单元特定的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，经验最优线性无偏预测（EBLUP）的均方预测误差（MSPE）通常会增大。观测最优预测（OBP）方法被提出，旨在改进EBLUP的MSPE。我们进行了蒙特卡洛模拟实验，以理解均值结构误设对不同小区域估计量的影响。我们的模拟结果得出一个意外结论：当使用观测单元层面的辅助变量时，OBP可能表现极差；而当在嵌套误差回归模型中使用这些辅助变量的总体均值（区域层面辅助变量）或使用相应的区域层面模型时，OBP可得到显著改进。我们的模拟还表明，OBP的MSPE是辅助变量的样本均值与总体均值之差的递增函数。