Model-Assisted Estimators with Auxiliary Functional Data

Few studies focus on the application of functional data to the field of design-based survey sampling. In this paper, the scalar-on-function regression model-assisted method is proposed to estimate the finite population means with auxiliary functional data information. The functional principal component method is used for the estimation of functional linear regression model. Our proposed functional linear regression model-assisted (FLR-assisted) estimator is asymptotically design-unbiased, consistent under mild conditions. Simulation experiments and real data analysis show that the FLR-assisted estimators are more efficient than the Horvitz-Thompson estimators under different sampling designs.