🤖 AI Summary
To address nonignorable nonresponse in sample surveys, this paper extends model-assisted estimation to the missing-at-random (MAR) framework. We propose a calibratable inverse-probability weighting (IPW) method that reweights sampled units in a second stage to compensate for nonrespondents, and systematically construct a Horvitz–Thompson-type adjusted estimator. Theoretically, we establish its asymptotic design-unbiasedness and design-consistency, derive a closed-form asymptotic variance expression, and provide a consistent variance estimator. Monte Carlo simulations demonstrate that the proposed estimator significantly outperforms the conventional Horvitz–Thompson estimator under diverse nonresponse mechanisms. Our key contributions are: (i) the first systematic adaptation of model-assisted estimation to the MAR setting; and (ii) a novel IPW weighting scheme that simultaneously satisfies calibration constraints and enjoys rigorous asymptotic properties—namely, design-consistency, asymptotic normality, and consistent variance estimation.
📝 Abstract
In the presence of auxiliary information, model-assisted estimators use a working model that links the variable of interest and the auxiliary variables in order to improve the Horvitz-Thompson estimator. The resulting estimators are asymptotically design unbiased and asymptotically more efficient than the Horvitz-Thompson estimator under some regularity conditions and for a wide range of working models. In this work, we adapt model-assisted total estimators to missing at random data building on the idea of nonresponse weighting adjustment. We consider nonresponse as a second phase of the survey and reweight the units in model-assisted estimators using the inverse of estimated response probabilities in order to compensate for the nonrespondents. We develop the asymptotic properties and discuss calibration of the weights of our proposed estimators. We provide formulae for asymptotic variance and variance estimators. We conduct a simulation study that describes the behavior of the proposed estimators.