Local polynomial regression estimators in survey sampling

Estimation of finite population totals in the presence of auxiliary informa tion is considered. A class of estimators based on local polynomial regress ion is proposed. Like generalized regression estimators, these estimators a re weighted linear combinations of study variables, in which the weights ar e calibrated to known control totals, but the assumptions on the superpopul ation model are considerably weaker. The estimators are shown to be asympto tically design-unbiased and consistent under mild assumptions. A variance a pproximation based on Taylor linearization is suggested and shown to be con sistent for the design mean squared error of the estimators. The estimators are robust in the sense of asymptotically attaining the Godambe-Joshi lowe r bound to the anticipated variance. Simulation experiments indicate that t he estimators are more efficient than regression estimators when the model regression function is incorrectly specified, while being approximately as efficient when the parametric specification is correct.