The Method Research On Model-assisted Sampling Estimation Based On Semi-parametric Product Adjustment

In sampling estimation,the superpopulation regression model describes the correlation between the auxiliary variables and the study variables.It makes the auxiliary variable directly into the estimator formula.Thus,it can significantly improve the estimation accuracy.The traditional generalized regression estimation assumes a linear relationship between the study variables and the auxiliary variables.But,the actual survey data seldom meet the linear relationship,so that the generalized regression estimator will perform inefficiently.In order to improve the sampling estimation accuracy,we firstly assume that the regression function of superpopulation model is a smooth function and propose a semi-parametric model.The fitted value of the model are achieved by semi-parametric product adjustment method.Then,a semi-parametric product adjustment estimator is carried out,together with its variance and variance estimator.It is proved that it has good statistical properties including asymptotic design-unbiasedness and design consistency.By means of simulation study,the estimator is proved to perform better than generalized regression estimator for those superpopulation models which are the lower linear degree.Studying the influence of parameter part of semi-parametric model on estimation precision,the parameter part of the semi-parametric regression model are extended to cubic function.Then,by means of simulation study,the estimator is proved to perform better than the semi-parametric estimator when the parameter part is linear function and the local polynomial regression estimator.Besides,the semi-parametric product adjustment estimation is combined with model-group.When the finite population can be divided into model-group,establishing model in each model-group can develop the accuracy of sampling estimation.