Local Polynomial Regression for Small Area Estimation

Estimation of small area means in the presence of area level auxiliary information is considered. A class of estimators based on local polynomial regression is proposed. The assumptions on the area level regression are considerably weaker than standard small area models. Both the small area mean functions and the between area variance function are modeled as smooth functions of area level covariates. A composite estimator that is a convex combination of the design weighted mean and the prediction from the non-parametric model is developed. The estimator is shown to be asymptotically consistent under mild regularity conditions. An approximation of the mean squared error (MSE) based on Taylor linearization is proposed.