基于半参数方法的模型辅助抽样估计研究

在总结现有模型辅助估计方法的基础上，本文通过构造一种半参数超总体模型，同时结合广义差分估计思想提出一种新型的模型辅助估计量。该估计量比传统的非参数和半参数回归估计利用更少、更易得到的辅助信息，即只需利用和广义回归估计相同的辅助信息，但一般会比广义回归估计拥有更高的估计精度。理论证明了该估计量是渐近设计无偏和设计一致的，其渐近设计均方误差为广义差分估计量的方差。模拟结果显示：其至少与广义回归估计一样好；对于线性程度越低的超总体模型，其估计精度比广义回归估计有越明显的提高；就本文模拟而言,光滑参数在0.04～0.12间适当取值时其会取到相对较好的估计效果。

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 superpopulation 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 nonparametric and semi-parametric regression estimators, but in general it is more accurate 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 superpopulation models linear degrees of which are the lower; in this simulation, smooth parameter which is properly selected between 0.04 and 0.12 can get good estimation effect relatively.