Generalised regression estimation given imperfectly matched auxiliary data

TL;DR

This paper develops three types of generalized regression estimators for survey sampling that can handle imperfect auxiliary data matching, maintaining design-based inference and enabling consistency testing and MSE estimation.

Contribution

It introduces novel estimators for survey sampling with imperfect auxiliary data, extending the applicability of generalized regression methods.

Findings

Estimators are consistent under certain conditions.

Mean square errors can be accurately estimated.

Simulation demonstrates estimator effectiveness.

Abstract

Generalised regression estimation allows one to make use of available auxiliary information in survey sampling. We develop three types of generalised regression estimator when the auxiliary data cannot be matched perfectly to the sample units, so that the standard estimator is inapplicable. The inference remains design-based. Consistency of the proposed estimators is either given by construction or else can be tested given the observed sample and links. Mean square errors can be estimated. A simulation study is used to explore the potentials of the proposed estimators.