A Unified Monte-Carlo Jackknife for Small Area Estimation after Model Selection

We consider estimation of measure of uncertainty in small area estimation (SAE) when a procedure of model selection is involved prior to the estimation. A unified Monte-Carlo jackknife method, called McJack, is proposed for estimating the logarithm of the mean squared prediction error. We prove the second-order unbiasedness of McJack, and demonstrate the performance of McJack in assessing uncertainty in SAE after model selection through empirical investigations that include simulation studies and real-data analyses.