A Study On Model-assisted Sampling Estimation Based On Semi-parametric Method

Based on the existing model-assisted estimation method, a new model-assisted estimator is proposed by a semi-parametric super-population model and the generalized difference estimation. The new estimator uses the same auxiliary information as the generalized regression estimator, which uses less and easier auxiliary information than the classical non-parametric and semi-parametric regression estimators, but in general it is more efficient than the generalized regression estimator.The new estimator can be proved to be asymptotically design-unbiased and design consistent, and its asymptotic design mean square error is the variance of the generalized difference estimator. Simulation experiments indicate the following results about the new estimator: It is never worse than the generalized regression estimator; its accuracy has more obvious improvement than the generalized regression estimator for those super-population models which are the lower linear degree; in this simulation, smooth parameter that properly selected between 0.04 and 0.12 can get good estimation effect in relative. At the same time, the validation of the actual data also shows that the new estimator is never worse than the generalized regression estimator, and much better in the‘income-life expectancy’ data. At last, this paper extend the proposed estimation method to the situation of the heteroscedastic super-population model and the multiple auxiliary variables and the two-stage sampling design which have three kinds of auxiliary information.