A one-bring-one route for assessing the uncertainty of small area estimation in nested-error regression models

The nested-error regression (NER) models are widely used to analyze unit-level data in small area estimation. Concerned about possible model misspecification, Jiang et al. (Surv Methodol 41:37–55, 2015) suggested a new prediction procedure, entitled observed best prediction (OBP), for the NER models and showed its desirable properties under such a setting. However, how to assess the uncertainty of OBP in such a case remains poorly addressed. This paper investigates this issue by developing a new estimator relying on the so-called one-bring-one route. It is shown that the new estimator is second-order unbiased under some mild conditions. Some simulations are conducted to confirm its finite sample performance. Finally, we applied the proposed estimator to a real-data example.