A predictive estimator of finite population mean using nonparametric regression (Q2430219)

An estimator is considered for the population mean by observations of the study variable \(y\) of sample units with an auxiliary variable \(x\) avaliable for all units from the (finite) population. The estimator is obtained as a linear combination of the sample mean and the mean of predictions for \(y\) made by \(x\) on the unobservable units. A nonparametric locally polynomial regression technique is used for the prediction. The estimator is compared to the Horvitz-Thompson, ratio, difference and classical parametric regression estimators via simulations. A cross-validation method for bandwidth selection in the regression estimator is discussed. Sociological real life data examples are presented.