Finite Population Model-Assisted Estimation Using Combined Parametric and Nonparametric Regression Smoothers

This paper considers estimating finite population totals from complex sample surveys in the presence of auxiliary information. Model-assisted estimators which assume a working regression model relating the study variable with the auxiliary data are common in this context. Both parametric and nonparametric working models have been utilized individually in constructing several model-assisted estimators. Model-assisted estimators with parametric working models are known to be efficient when the assumed working model is correctly specified, while using nonparametric smoothers gives more robust estimates but requires relatively large sample sizes. In this paper, we consider the situation where the researcher has an idea of which parametric model can describe the relationship between the study variable and the auxiliary data, but this model may not be adequate in some areas of the data range. Using combined parametric and nonparametric regression smoothers for the working model, we introduce a new class of model-assisted estimators for finite population totals. The proposed estimators are shown to have the desirable asymptotic properties of traditional model-assisted estimators of population totals. The finite sample performance of the new estimators is studied via Monte Carlo simulations from both artificial and real populations. The empirical results suggest that our proposed estimators perform well relative to other model-based and model-assisted estimators as well as the customary Horvitz–Thompson estimator under different levels of misspecification in the working model. We also discuss the problem of variance estimation for the proposed estimators.