Research On Model Averaging Assisted Sampling Estimation Method And Its Application

In the context of big data,it is easier to obtain more available auxiliary information,which helps to improve the accuracy of sampling estimation.In order to use auxiliary information in sampling estimation,the traditional method is to establish a super population regression model between research variable and auxiliary variables,so as to adjust and improve the randomized estimation results based on design.This method is called model-assisted sampling estimation method.Among them,whether the established regression model is appropriate and whether the estimation of the model is reasonable will be the key to determine whether the model assisted sampling estimation method can improve the estimation accuracy or how much the accuracy can be improved.Existing studies have set up different models to better fit the relationship between research variable and auxiliary variables.However,the selection of auxiliary variables in the modeling process is ignored.It usually relies on human experience or traditional model selection methods to select a single model for assisting sampling estimation.Obviously,there is a risk of model uncertainty in this practice.At the same time,some useful information will be deleted,and the auxiliary role of the model may be greatly reduced,which will lead to little or no improvement in the accuracy of sampling estimation.For such problems,a feasible idea is to combine multiple better models for assisting sampling estimation.Therefore,this paper introduces the model averaging method into the framework of model-assisted sampling estimation.By setting reasonable model weights to combine multiple models for auxiliary estimation,not only the single model selection bias can be avoided,but also the effective auxiliary information can be utilized to the maximum extent,so as to improve the sampling estimation efficiency robustly and effectively.Specifically,this paper mainly includes the following aspects:First,aiming at the problems of the single model-assisted sampling estimation,a model averaging method is introduced to build the model averaging assisted sampling estimator.In the first place,under the common super population regression model,combined with the linear model averaging method,this paper proposes the linear model averaging assisted sampling estimator according to the idea of generalized difference estimation,and proves theoretically that the estimator is asymptotically design unbiased and design consistent.Next,it is verified by numerical simulation that the linear model averaging auxiliary estimation is better than the single model assisted sampling estimation,especially when there is interference information.Finally,the results of sampling estimation through the actual data also verify that the estimator proposed in this paper can better solve the uncertainty problem in the super population model modeling and effectively improve the effect of sampling estimation.Secondly,for the case of high-dimension auxiliary variables,the Bayesian model averaging assisted sampling estimator is proposed.The linear super population regression model is estimated by Bayesian model averaging.And combined with the generalized difference estimation method,the Bayesian model averaging assisted sampling estimator is constructed,and its statistical properties are proved.The results of further numerical simulation show that the Bayesian model averaging assisted sampling estimation has obvious advantages over the single model assisted sampling estimation and conforms to the asymptotic theory.Finally,the actual data verification results confirm this conclusion again.Thirdly,aiming at the coexistence of two types of model uncertainty problems: variable selection and model form setting,the partial linear model averaging assisted sampling estimator is constructed.In the first place,the idea of model averaging for partial linear model is proposed,and the method of partial linear model averaging is given.Next,the super population regression model is estimated by using the partial linear model averaging,and the partial linear model averaging assisted estimator and its asymptotic properties are given in the framework of generalized difference estimation.Finally,the simulation analysis and actual data verification are carried out for the two cases of non-parametric structure determination and uncertainty respectively.The results show that the partial linear model averaging assisted sampling estimation is superior to the single model assisted sampling estimation regardless of whether the non-parametric variables are fixed.When the global function is nonlinear,the former advantage is more prominent.Fourthly,in order to apply social network auxiliary information to sampling estimation,the network model averaging assisted sampling estimator is constructed.In the first place,the super population regression regression model is set as the network model,and the two kinds of network model averaging method are given.Similarly,under the framework of generalized difference estimation,the network model averaging assisted sampling estimator is proposed.Next,the simulation analysis is carried out under different network compositions and different network objective functions.The results show that the network model averaging assisted sampling estimation is better than the model-assisted sampling estimation without considering social network information,and also better than single network model assisted estimation.Fifthly,this paper discusses the specific application path of model averaging assisted estimation method in China.First of all,on the basis of reviewing the development process of China’s statistical survey system,this paper points out the existing problems affecting the quality of sampling estimation and restricting the further development of sampling estimation,and puts forward the general application idea of model averaging assisted sampling estimation method.Next,some specific measures are put forward to solve the outstanding problems existing in the implementation of model averaging assisted sampling estimation.Finally,considering the specific implementation of model averaging assisted sampling estimation in various situations,and combined with the real situation of small enterprises sampling estimation,the practical guidance of model averaging assisted sampling estimation method is given in detail.In general,this paper introduces the model averaging method into the framework of modelassisted sampling estimation,and extends the traditional single model assisted sampling estimation to the combined model assisted sampling estimation,which can not only improve the estimation accuracy effectively and robustly,but also promote the integration of sampling estimation method and big data.It has important reference significance to construct the highquality statistical survey system in line with the requirements of the new era.