The mean squared error of small area predictors constructed with estimated area variances
成果类型：
Article
署名作者：
Wang, JY; Fuller, WA
署名单位：
Merck & Company; Merck & Company USA; Iowa State University
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1198/016214503000000620
发表日期：
2003
页码：
716-723
关键词：
摘要：
In the small area estimation literature, the sampling error variances are customarily assumed to be known or to depend on a finite number of parameters. We consider the empirical best linear unbiased predictor (EBLUP) obtained by using the individual directly estimated variance for each small area. An approximation for the mean squared error (MSE) of the EBLUP that recognizes the impact on the predictors of estimation of the variance components is derived. Simulation studies show that the theoretical expressions are good approximations for the MSE of the predictors unless the between-area variance component is very small (relative to the within-area variance). An improved estimator of the MSE is developed that has smaller overestimation than the original estimator when the between-area variance component is small. The robustness of the MSE estimator is studied and predictors for nonnormal sampling errors are proposed. An example from the National Resources Inventory that motivated the development of the theory is described.
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