基于惩罚样条回归的模型校准估计方法
|
摘要
传统的广义回归抽样估计方法有一个严格的假设条件,即研究变量和辅助变量之间呈现线性关系,因此在非线性情形下的估计效果并不理想,而基于模型校准的抽样估计方法则能克服这种缺陷,可以较好地提升估计量的估计精度。文章在梳理已有的非参数超总体模型基础上,结合惩罚样条回归与模型校准估计法,介绍了一种新的基于惩罚样条回归的非参数模型校准估计方法,并在一定的设计条件下阐明了该估计量在模型辅助情况下具有渐近无偏性和服从渐近正态分布等优良性质。进一步的模拟研究结果显示,经过校准的估计量比未校准的估计量具有更高的估计精度,且在超总体模型中,随着非线性程度的增强,该估计量的估计精度比参数估计量有显著的提高。
The traditional generalized regression sampling estimation method has a strict assumption that there is a linear relationship between research variables and the auxiliary variables. Therefore, the estimation effect in the nonlinear case is not ideal,and the sampling estimation method based on model calibration can overcome this defect and improve the estimation accuracy of estimators. In this paper, on the basis of combing the existing non-parametric super-population model, the author introduces a new non-parametric model calibration estimation method based on penalty spline regression. Under certain design conditions, the paper expounds that the estimator is asymptotically unbiased and obeys asymptotically normal distribution in the model-assisted case. Further simulation results show that the calibrated estimator has higher estimation accuracy than the uncalibrated estimator,and in the super-population model, with the enhancement of the nonlinear degree, the estimation accuracy of the estimator is significantly improved than that of the parameter estimator.
The traditional generalized regression sampling estimation method has a strict assumption that there is a linear relationship between research variables and the auxiliary variables. Therefore, the estimation effect in the nonlinear case is not ideal,and the sampling estimation method based on model calibration can overcome this defect and improve the estimation accuracy of estimators. In this paper, on the basis of combing the existing non-parametric super-population model, the author introduces a new non-parametric model calibration estimation method based on penalty spline regression. Under certain design conditions, the paper expounds that the estimator is asymptotically unbiased and obeys asymptotically normal distribution in the model-assisted case. Further simulation results show that the calibrated estimator has higher estimation accuracy than the uncalibrated estimator,and in the super-population model, with the enhancement of the nonlinear degree, the estimation accuracy of the estimator is significantly improved than that of the parameter estimator.
引文
[1]Chambers R L,Dorfman A H,Wehrly T E.Bias Robust Estimation in Finite Populations Using Nonparametric Cali Bration[J].Journal of the American Statistical Association,1993,(88).
[2]Montanar G E,Ranalli M G.Nonparametric Model Calibration Estimation in Survey Sampling[J].Journal of the American Statistical Association,2005,100(472).
[3]Deville J C,S?rndal C E.Calibration Estimators in Survey Sampling[J].Journal of the American Statistical Association,1992,87(418).
[4]Wu C,Sitter R R.A Model-calibration Approach to Using Complete Auxiliary Information from Survey Data[J].Journal of the American Statistical Association,2001,96(453).
[5]Eilers P H C,Marx B D.Flexible Smoothing With B-splines and Penalties[J].Statistical Science,1996,11(2).
[6]Zheng H,Little R J A.Penalized Spline Model-based Estimation of the Finite Population Total From Probability Proportional-to-size Samples[J].Journal of Official Statistics,2003,(19).
[7]Breidt F J,Claeskens O.Model-Assisted Estimation for Complex Surveys Usingpenalised splines[J].Biometrika,2005,(92).
[8]Montanari G E,Ranalli M G.A Mixed Model-Assisted Regression Estimator That Uses Variables Employed at the Design Stage[J].Statistical Methods and Applications,2006,(15).
[9]Opsomer J D,Claeskens G,Ranalli M G,et al.Non-Parametric Small Area Estimation using Penalized Spline Regression[J].Journal of the Royal Statistical Society:Series B(Statistical Methodology),2008,(70).
[10]Isaki C T,Fuller W A.Survey Design Under the Regression Superpopulation Model[J].Journal of the American Statistical Association,1982,,(77).
[2]Montanar G E,Ranalli M G.Nonparametric Model Calibration Estimation in Survey Sampling[J].Journal of the American Statistical Association,2005,100(472).
[3]Deville J C,S?rndal C E.Calibration Estimators in Survey Sampling[J].Journal of the American Statistical Association,1992,87(418).
[4]Wu C,Sitter R R.A Model-calibration Approach to Using Complete Auxiliary Information from Survey Data[J].Journal of the American Statistical Association,2001,96(453).
[5]Eilers P H C,Marx B D.Flexible Smoothing With B-splines and Penalties[J].Statistical Science,1996,11(2).
[6]Zheng H,Little R J A.Penalized Spline Model-based Estimation of the Finite Population Total From Probability Proportional-to-size Samples[J].Journal of Official Statistics,2003,(19).
[7]Breidt F J,Claeskens O.Model-Assisted Estimation for Complex Surveys Usingpenalised splines[J].Biometrika,2005,(92).
[8]Montanari G E,Ranalli M G.A Mixed Model-Assisted Regression Estimator That Uses Variables Employed at the Design Stage[J].Statistical Methods and Applications,2006,(15).
[9]Opsomer J D,Claeskens G,Ranalli M G,et al.Non-Parametric Small Area Estimation using Penalized Spline Regression[J].Journal of the Royal Statistical Society:Series B(Statistical Methodology),2008,(70).
[10]Isaki C T,Fuller W A.Survey Design Under the Regression Superpopulation Model[J].Journal of the American Statistical Association,1982,,(77).