Semiparametric Small Area Estimation of Crop Acreage under Partially Linear Model

We propose the semiparametric small area estimator under the partially linear model. Unlike the linear mixed models widely used in the small area estimation, which assume that the area effect is the random effect, we model the area effect as the unknown function of an area-indicative variable. We represent the nonparametric part for area effect using penalized splines, by which the estimation and inference are done in the linear mixed model framework. The mean-squared error of empirical estimators is shown and the testing for small area effect also considered. The agricultural application of this modeling shows our proposed method could get the reliable estimates. Additionally, some numerical simulations are demonstrated to express the good performance of this modeling.