Quasi-model-assisted estimators under nonresponse in sample surveys

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. • Introduces a unified framework for model-assisted estimation with nonresponse. • Couples working and response models to strengthen robustness to misspecification. • Unifies many known estimators as special cases within one broad framework. • Extends doubly robust methods to complex survey designs with nonresponse. • Simulations show low bias and variance even under model misspecification.