Quasi Model-Assisted Estimators under Nonresponse in Sample Surveys

TL;DR

This paper introduces quasi-model-assisted estimators for survey nonresponse, combining a working model and a response model to improve efficiency and robustness, supported by simulation results.

Contribution

It extends model-assisted estimators to nonresponse settings by integrating two models, allowing flexible use of statistical learning methods and demonstrating robustness.

Findings

Estimators remain competitive with poorly specified models.

Simulation shows improved bias and variance performance.

Several existing estimators are special cases of the proposed class.

Abstract

In the presence of auxiliary information, model-assisted estimators rely on a working model linking the variable of interest to the auxiliary variables in order to improve the efficiency of the Horvitz-Thompson estimator. Model-assisted estimators cannot be directly computed with nonresponse since the values of the variable of interest is missing for a part of the sample units. In this article, we present and study a class of quasi-model-assisted estimators that extend model-assisted estimators to settings with non-ignorable nonresponse. These estimators combine a working model and a response model. The former is used to improve the efficiency, the latter to reweight the nonrespondents. A wide range of statistical learning methods can be used to estimate either of these models. We show that several well-known existing estimators are particular cases of quasi-model-assisted estimators. We examine the behavior of these estimators through a simulation study. The results illustrate how these estimators remain competitive in terms of bias and variance when one of the two models is poorly specified.