Two stage non-parametric approach for small area estimation

Small area estimators commonly borrow strength from other related areas. These indirect estimators use models (explicit or implicit) that relate the small areas through supplementary data. Various unit-level and area-level small area models are proposed in the literature, but all these models assume the small area mean is linearly related with supplementary information. In this article, we propose an area-level, nonparametric regression estimator based on NadarayaWatson kernel on small area mean. In this direction, we adopt a two-stage estimation approach proposed by Prasad and Rao (1990). The asymptotic properties of the proposed estimator are studied and a second order approximation to the mean squared prediction error (MSPE) of the two-stage estimator and the estimator of MSPE approximation are obtained under normality. We perform a simulation study to show the superiority of the proposed estimator and finally we apply this smoothing method to estimate soil loss due to erosion in certain mid-western counties in U.S.