Model Calibration Sampling Estimation Based On Smoothing Spline Method

Recently,calibration estimation has played an important role in the field of sampling investigations as well as the theory and practice of sampling surveys at home and abroad.As the traditional calibration estimation method is suitable for the linear relationship between the research variable and the auxiliary variable,when the research variables are nonlinearly related to the auxiliary variables,the estimation accuracy of the estimators obtained by the traditional calibration estimation method is not high,while smooth spline model calibration estimator can solve this problem well.Firstly,a super population model was established to describe the relationship between research variables and auxiliary variables.Then using nonparametric estimation of original smooth sample to estimate the mean function model to get the fitting values,finally combine the mean function fitting in the form of value calibration estimation to get smooth spline model calibration estimators.Chapter 1 introduces the background and significance of the topic in detail,as well as the research status of calibration estimates and model calibration estimators both theoretically and practically at home and abroad.Chapter 2 introduces the expression of the traditional calibration estimator,discusses the properties of the calibration estimator,and reviews the definition of the spline function,the expres-sion of the smooth spline estimator and the selection of smooth parameters in the spline estimation.Chapter 3 introduces the expression and properties of the model calibration estimator,and proposes a new model calibration estimator,which is the smooth spline model calibration estimator,and gives its expression and properties as well.In chapter 4,when there is a linear relationship and a nonlinear relationship between the research variable and the auxiliary variable respectively,Comparing the accuracy of the traditional calibration estimator and the estimation accuracy of the smoothing spline model estimator through data simulation method,When the relationship between them is nonlinear,the precision of the smooth spline model calibration estimator is higher than the traditional calibration estimator.In chapter 5,it summarizes the content of this paper and proposes further research directions.