Single-Index Model-Assisted Estimation In Survey Sampling

TL;DR

This paper introduces a semiparametric single-index model-assisted estimation method for survey sampling that improves accuracy by leveraging auxiliary information and demonstrates strong theoretical and empirical performance.

Contribution

It proposes a robust, efficient polynomial spline-based estimator using a single-index model, applicable to large survey datasets with proven asymptotic properties.

Findings

Estimator is asymptotically unbiased and normal

Method performs well on simulated and real datasets

Provides fast analysis suitable for large data

Abstract

A model-assisted semiparametric method of estimating finite population totals is investigated to improve the precision of survey estimators by incorporating multivariate auxiliary information. The proposed superpopulation model is a single-index model which has proven to be a simple and efficient semiparametric tool in multivariate regression. A class of estimators based on polynomial spline regression is proposed. These estimators are robust against deviation from single-index models. Under standard design conditions, the proposed estimators are asymptotically design-unbiased, consistent and asymptotically normal. An iterative optimization routine is provided that is sufficiently fast for users to analyze large and complex survey data within seconds. The proposed method has been applied to simulated datasets and MU281 dataset, which have provided strong evidence that corroborates with the asymptotic theory.