基于局部多项式回归的模型校准抽样估计研究  

Research on Model Calibration Estimator in Survey Sampling Based on Local Polynomial Regression

作　　者：马志华[1] 陈光慧[1] 

机构地区：[1]暨南大学经济学院,广东广州510632

出　　处：《数理统计与管理》2016年第1期47-56,共10页Journal of Applied Statistics and Management

基　　金：国家社会科学基金青年项目(14CTJ014);中央高校基本科研业务费专项资金(暨南启明星计划)项目(12JNQM006)

摘　　要：在抽样估计中,当研究变量与辅助变量之间呈非线性关系时,传统的校准估计方法效果较差,基于非参数回归方法的模型校准估计量则可以很好地解决这一问题。首先,建立描述研究变量和辅助变量之间关系的超总体回归模型,使用非参数中的局部多项式方法得出模型参数的拟合值,并结合校准估计得出局部多项式模型校准估计量,同时给出其方差和方差估计量公式,证明了该估计量具有渐近无偏性、一致性和渐近正态性等优良的统计性质。然后,使用仿真模拟的方法证明在研究变量与研究变量之间呈非线性关系时,该估计量有良好的估计效果。最后,对该估计量在我国政府统计中的应用进行简单的介绍。In sampling estimation, when there is a non-linear relationship between the survey variable and auxiliary variables, calibration estimators would perform inefficiently, while which can be well solved by model calibration estimation based on nonparametric regression. In t his paper, firstly a superpop- ulation model describing the relationship between the survey variable and auxiliary variables is built, after which the fitted values of the parameters are achieved by nonparametric regression method, called the local polynomials. Combining with calibration estimation, a local polynomial model calibration es- timator is carried out, together with its variance and variance estimator. Also, it is proved that it has good statistical properties including asymptotic unbiasedness and consistency, asymptotic normality. By means of simulation study, the estimator is proved to perform well when there is a nonlinear relationship between the survey variable and the auxiliary variable. At last, an introduction of its application in government statistics is also carried out.

关 键 词：抽样估计 超总体模型 非参数回归 校准估计 局部多项式回归 

分 类 号：O212[理学—概率论与数理统计]