Small Area Mean Estimation Based On Density Ratio Model

Since most sampling surveys are designed to obtain only the overall information,it is easy to make the sample allocation on some sub-populations less,resulting in the estimation of these sub-populations parameters cannot meet the accuracy requirement.At the unit level,it is a common method for small area estimation in recent years by establishing a suitable model to mine common information between sub-populations and using the extracted information to improve the accuracy of parameter estimation of small sample sub-populations.However,the existing methods usually assume that the error terms in the model are independent of each other,which is not realistic at many times,and the density ratio model can effectively describe the correlation between subpopulations error terms.In this paper,the problem of small area mean estimation is studied under the assumption that the error term obeys the density ratio model.The main contents are as follows:Firstly,under the assumption that the error term of nested error linear regression model obeys the density ratio model,the error distribution function of each small area is estimated by empirical likelihood method,and then the distribution function of the sub-population target variable is estimated,and the mean of each small area is estimated by the distribution function.The numerical simulation results show that the mean estimation given by this method has smaller deviation and mean square error.Secondly,based on the nested error nonparametric model,the small area mean estimation is studied under the assumption that the error term obeys the density ratio model.Firstly,the non-parametric function is fitted by the penalty spline,then the error distribution function is estimated by the empirical likelihood method based on the fitting residual,and the distribution function of the sub-population target variable is further estimated,and then the distribution function of the target variable is used to estimate the mean of each small area.The numerical simulation results show that,the new method can significantly improve the estimation accuracy compared with direct estimation,but the result is worse than that of the linear model.In addition,it is also found that the selection of the basis function in the density ratio model has a significant effect on the linear model,but has little effect on the non-parametric model.Finally,the proposed method was used to study the small area estimation of personal income in a group of Canadian population sample survey data.