In this paper, the estimation for finite population total of a study variable will be considered, and the local linear regression will be used. The study variable is available for the sample and is supplemented by two auxiliary variables, which are available for every element in the finite population. Also, the resampling methods will be combined with the local linear regression method to estimate the total. The comparisons between different methods will be performed based on the mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). A simulation study is carried out to assess the effects.

The nonparametric regression estimator for the finite population total under twostage sampling is introduced using a new technique. In stage one, a sample of clusters is selected and in stage two, sub samples of elements within each selected cluster are obtained. The auxiliary variable is available for all elements in the population and the nonparametric model describes the relationship between the study variable and the auxiliary variable. The kernel and local linear regression is used in the estimation of total without using the expressions of the inclusion probabilities and three scenarios are proposed to estimate the finite population total. The comparison between the two nonparametric methods is performed based on the mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). Also, a comparison between the three scenarios is done. These comparisons are performed using a simulation study.

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