Nonparametric Regression Estimation of Finite Population Totals under Two-Stage Sampling

We consider nonparametric regression estimation for finite population totals for two-stage sampling, in which complete auxiliary information is available for first-stage sampling units. The estimators, based on local polynomial regression, are linear combinations of cluster total estimators, with weights that are calibrated to known control totals. The estimators are asymptotically design-unbiased and design consistent under mild assumptions. We provide a consistent estimator for the design mean squared error of the estimators. Simulation results indicate that the nonparametric estimator dominates standard parametric estimators when the model regression function is incorrectly specified, while being nearly as efficient when the parametric specification is correct. The methodology is illustrated using data from a study of land use and erosion. ∗Department of Statistics, Iowa State University, Ames IA 50011, USA. †Department of Statistics, Colorado State University, Fort Collins CO 80523, USA, [email protected]. ‡Department of Statistics, Colorado State University, Fort Collins CO 80523, USA, [email protected].