Local Polynomial Regression Estimation in Two-stage Sampling

We consider local polynomial regression estimation for nite population totals in two-stage element sampling. The estimators are linear combinations of es-timators of cluster totals with weights that are calibrated to known control totals. The estimators are asymptotically design-unbiased and consistent under mild assumptions. We provide a consistent es-timator for the design mean squared error of the local polynomial regression estimators. Simulation results show that the estimators are more eecient than Horvitz-Thompson and linear regression esti-mators when the mean function of the superpopu-lation model is non-linear while being nearly as ee-cient when the model is linear. The estimation approach performs well in an example using data from a 1995 study associated with the National Resources Inventory.