基于测量误差的Fay-Herriot模型在小域估计中的应用研究

Application of Fay-Herriot Model Based on Measurement Error in Small Area Estimation

Fay-Herriot模型是常用的小域估计模型方法之一。但传统的Fay-Herriot模型未能考虑模型中辅助信息的测量误差问题,这将会影响目标估计量的估计精度。考虑到辅助信息中可能出现测量误差的情形,构建适应性更佳的基于测量误差的Fay-Herriot模型来进行小域估计。首先,利用结构误差模型来关联小域直接估计量和辅助信息,将小域估计模型转化为测量误差模型;其次,采用广义最小二乘法得到小域目标参数的最优线性无偏估计;最后,利用迭代广义最小二乘法来估计模型的未知参数。该模型不仅解决了辅助信息测量误差方差计算困难的问题,同时也提高了小域估计量的稳定性。数值模拟结果显示,与其他Fay-Herriot估计量相比,在辅助信息存在测量误差的小域中,基于测量误差模型的Fay-Herriot估计量均方误差普遍较小,表现也更为稳健。

Fay-Herriot model is one of the commonly used small area estimation methods.However,the traditional Fay-Herriot model fails to consider the measuring error of auxiliary information,that may affect the precision of target estimator.Considering the possible measuring error of auxiliary information,it has vital practical significance that a better adaptive Fay-Herriot model based on measuring error is constructed in small area estimation.Firstly,it links the small area direct estimator and the auxiliary information with the structural error model.Therefore,the model for small area estimation can be regarded as a measuring error model.Secondly,the generalized least square method is used to obtain the best linear unbiased predictor of the small area parameter.Finally,the iterative generalized least square method is used to estimate the parameters.The model not only solves the difficulties of calculating the measuring error variance of auxiliary information,but also improves the stability of small area estimator.The numerical simulation and analysis show that,compared with other Fay-Herriot estimators,the mean square error of the Fay-Herriot estimator based on measuring error is generally slighter and more stable.