A model based survey is employed to estimate the unknown values of the survey variable, using the local linear regression approach. In particular, a local linear regression estimator in model based surveys is studied. Variance comparisons are made between the derived estimator and the Nadaraya-Watson regression estimator which show that the two estimators are asymptotically equivalently efficient.

survey sampling, auxiliary information, local linear regression estimator, model based surveys, nonparametric regression, asymptotic relative efficiency.