Small Area Estimation with Random Effects Selection

In this study, we propose a robust method holding a selective shrinkage power for small area estimation with automatic random effects selection referred to as SARS. In our proposed model, both fixed effects and random effects are treated as joint target. In this case, maximizing joint likelihood of fixed effects and random effects makes more sense than maximizing marginal likelihood. In practice, variance of sampling error and variance of modeling error (random effects) are unknown. SARS does not require any prior information of both variance components and dimensionality of data. Furthermore, area-specific random effects, accounting for additional area variation, are not always necessary in small area estimation model. From this observation, we can impose sparsity on random effects by assigning zero for the large area. This sparsity brings heavy tails, which means that the normality assumption of random effects is not retained any longer. The SARS holding selective and predictive power employs penalized regression using a non-convex penalty. For solving the non-convex problem of SARS, we employ iterative algorithms via a quantile thresholding procedure. The algorithms make use of the iterative selection-estimation paradigm with a variety of techniques such as progressive screening when tuning parameters, muti-start strategy with subsampling method and feature subset method to generate more efficient initial points for enhancing computation efficiency and efficacy. To achieve optimal prediction error under the dimensional relaxation, we propose a new theoretical predictive information criterion for SARS (SARS-PIC) which is derived based upon non-asymptotic oracle inequalities using minimax rate of ideal predictive risk. Experiments with simulation and real poverty data of school-age(5-17) children demonstrate the efficiency of SARS.