Estimating the mean squared prediction error of the observed best predictor associated with small area counts: A computationally oriented approach

We consider estimation of the mean squared prediction error (MSPE) for observed best prediction (OBP) in small area estimation with count data. The OBP method has been previously developed in this context by Chen et al. (Journal of Survey Statistics and Methodology, 3, 136–161, 2015). However, estimation of the MSPE remains a challenging problem due to potential model misspecification that is considered in this setting. The latter authors proposed a bootstrap method for estimating the MSPE, whose theoretical justification is not clear. We propose to use a Prasad–Rao-type linearization method to estimate the MSPE. Unlike the traditional linearization approaches, our method is computationally oriented and easier to implement in the same regard. Theoretical properties and empirical performance of the proposed method are studied. A real-data application is considered.