Clustering in Small Area Estimation with Area Level Linear Mixed Models
提出通过聚类小区域来改进区域均值预测的均方误差，并给出统计检验和二阶无偏估计量，适用于样本稀少时的可靠估计。
Summary Finding reliable estimates of parameters of subpopulations (areas) in small area estimation is an important problem especially when there are few or no samples in some areas. Clustering small areas on the basis of the Euclidean distance between their corresponding covariates is proposed to obtain smaller mean-squared prediction error (MSPE) for the predicted values of area means by using area level linear mixed models. We first propose a statistical test to investigate the homogeneity of variance components between clusters. Then, we obtain the empirical best linear unbiased predictor of small area means by taking into account the difference between variance components in different clusters. We study the performance of our proposed test as well as the effect of the clustering on the MSPE of small area means by using simulation studies. We also obtain a second-order approximation to the MSPE of small area means and derive a second-order unbiased estimator of the MSPE. The results show that the MSPE of small area means can be improved when the variance components are different. The improvement in the MSPE is significant when the difference between variance components is considerable. Finally, the methodology proposed is applied to a real data set.