Semiparametric Small Area Estimation of Crop Acreage under Partially Linear Model

TL;DR

This paper introduces a semiparametric approach for small area estimation of crop acreage, modeling area effects as unknown functions with penalized splines within a linear mixed model framework, enhancing flexibility and inference.

Contribution

It proposes a novel semiparametric model for small area effects using penalized splines, extending traditional linear mixed models for better flexibility.

Findings

The method performs well in numerical simulations.

The mean-squared error of estimators is derived.

Testing procedures for small area effects are developed.

Abstract

Small area estimation under linear mixed models often assumes that the small area effect is random effect in almost all previous studies. However, in this paper a new approach is proposed explaining small area effect as the unknown function of an area-indicative variable, which is a kind of semiparametric models. The nonparametric part for area effect is represented by using penalized splines, from 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. Additionally, some numerical simulations are demonstrated to express the good performance of this method.