Geographically weighted regression model-assisted estimation in survey sampling

A geographically weighted regression model-assisted method is proposed to estimate the finite population totals using survey data with the aid of spatial and other auxiliary information. The local linear method is used to the estimation of geographically weighted regression model. Our proposed GWR-assisted (geographically weighted regression model-assisted) estimators are more efficient than the well-known Horvitz-Thompson estimators. These estimators are calibrated and asymptotically design-unbiased. Some theoretical results have been established for GWR-assisted estimators. Simulation experiments show that the GWR-assisted estimators are more efficient than the LM-assisted (linear regression model-assisted) estimators and NP-assisted (nonparametric regression model-assisted) estimators. Finally, the Boston housing data are used in the simulation study to demonstrate the importance of location information in spatial modelling.