Nonparametric Additive Model-assisted Estimation for Survey Data

TL;DR

This paper introduces a nonparametric additive model-assisted estimation method for survey data that improves precision, is computationally efficient for large high-dimensional datasets, and includes a variable selection procedure.

Contribution

It develops a novel additive model-assisted estimator combining spline and local polynomial smoothing, with a consistent variable selection method, enhancing survey data analysis accuracy and speed.

Findings

Estimator is asymptotically unbiased and normal.

Method attains the Godambe-Joshi lower bound.

Performs well in simulation studies.

Abstract

An additive model-assisted nonparametric method is investigated to estimate the finite population totals of massive survey data with the aid of auxiliary information. A class of estimators is proposed to improve the precision of the well known Horvitz-Thompson estimators by combining the spline and local polynomial smoothing methods. These estimators are calibrated, asymptotically design-unbiased, consistent, normal and robust in the sense of asymptotically attaining the Godambe-Joshi lower bound to the anticipated variance. A consistent model selection procedure is further developed to select the significant auxiliary variables. The proposed method is sufficiently fast to analyze large survey data of high dimension within seconds. The performance of the proposed method is assessed empirically via simulation studies.