Observed best selective prediction in small area estimation

In small area estimation methodology, selection of the suitable covariates and estimation in the selected model are usually considered separately. In this paper, we consider variable selection and estimation simultaneously to minimize the total mean squared prediction errors (MSPE)for estimation of small area means. The derived method, which we call observed best selective prediction (OBSP), can be regarded as an extension of the observed best prediction (OBP)method by Jiang et al. (2011). When the true model is included in the largest model, the resulting OBSP estimator is consistent. Based on the asymptotic result, we derive an estimator of MSPE by applying the parametric bootstrap method. Through simulation experiments, we investigate the finite-sample performance of OBSP together with OBP in which the variable selection is carried out by using AIC and BIC, and OBP using all the covariates. As an example, we applied OBSP to Japanese survey data.