Small area estimators based on restricted mixed models

Abstract

This paper proposes a new model-based approach to estimate small areas that extends the Fay–Herriot methodology. The new model is additive, with a random term to characterize the inter-area variability and a nonparametric mean function specification, defined using the information on an auxiliary variable. The most significant advantage of the proposal is that it avoids the model misspecification problem. The monotonicity is the only assumption about the functional form of the relationship between the variable of interest and the auxiliary one. Estimators for the area means are derived combining “Order Restricted Inference” and standard mixed model approaches. A large simulation experiment shows how the new approach outperforms the Fay–Herriot methodology in many scenarios. Besides, the new method is applied to the Australian farms data.