A class of general adjusted maximum likelihood methods for desirable mean squared error estimation of EBLUP under the Fay-Herriot small area model

摘要

The empirical best linear unbiased prediction (EBLUP) estimator is utilized for efficient inference in various research areas, especially for small-area estimation. In order to measure its uncertainty, we generally need to estimate its mean squared prediction error (MSE). Ideally, an EBLUP-based method should not only provide a second-order unbiased estimator of MSE of EBLUP but also maintain strict positivity in estimators of both model variance parameter and MSE of EBLUP. Fortunately, the MSE estimators proposed in Yoshi-mori and Lahiri (2014) and Hirose and Lahiri (2018) achieve the three desired properties simultaneously. As far as we know, no other MSE estimator does so.