Abstract: In survey sampling, model-assisted approach is often used to improve the precision of survey estimators when auxiliary information is available. Generally, the model-assisted estimators are nonlinear functions of some classical Horvitz–Thompson estimators constructed via inverse probability weighting, which are seriously affected by the heterogeneous inclusion probabilities. In this paper, we improve the classical model-assisted estimation via probability thresholding, and propose the improved linear and nonparametric model-assisted estimators for finite populations. The proposed estimators are shown to be asymptotically design unbiased and design consistent. The corresponding design mean squared errors and their estimators are also derived. We theoretically prove that the new model-assisted estimators are asymptotically not worse than the commonly used model-assisted estimators. Two simulation examples and an empirical application indicate good finite sample performance of the proposed estimators.

Key words and phrases: Horvitz–Thompson estimator, model-assisted estimation, probability thresholding, superpopulation model, survey sampling.