华东师范大学学报(自然科学版) ›› 2005, Vol. 2005 ›› Issue (3): 31-36.

• 数学 统计学 • 上一篇    下一篇

EV回归的半参数部分线性模型的Bayes估计

卢一强1, 2，茆诗松2   

  1. 1.解放军信息工程大学 电子技术学院，郑州450004;2.华东师范大学 统计系，上海200062
  • 收稿日期:2003-01-14 修回日期:2003-06-02 出版日期:2005-08-25 发布日期:2005-08-25
  • 通讯作者: 卢一强

Bayesian Estimation in A Semiparametric Partially Linear Errors-in-variable Model(Chinese)

LU Yi-qiang1, 2,MAO Shi-song2   

  1. 1.Institute of Electronic Technology, the PLA Information Engineering University，Zhengzhou450004,China;2.Department of Statistics, East China Normal University, Shanghai200062,China
  • Received:2003-01-14 Revised:2003-06-02 Online:2005-08-25 Published:2005-08-25
  • Contact: LU Yi-qiang

摘要： 考察部分线性模型y=Xτβ+g(t)+ε,ε~N(0,σ2),其中回归变量X可以精确测量，而t具有测量误差. 用光滑样条估计非参数函数g(t), 结合光滑样条的Bayes解释及Bayes的线性回归, 将模型中的未知参数赋以一定的先验, 运用Gibbs抽样方法从后验分布中抽样, 用后验样本的均值来估计未知参数. MCMC模拟的另外一个好处是容易从后验样本中构造后验样本区间估计. 最后,提供了一个模拟例子来说明Bayes方法的估计效果.

关键词: 部分线性模型, 光滑样条, EV回归, Bayes方法, Gibbs抽样, MCMC模拟, 部分线性模型, 光滑样条, EV回归, Bayes方法, Gibbs抽样, MCMC模拟

Abstract: This article deals with the partially linear model y=Xτβ+g(t)+ε, where ε~N(0,σ2), the predictor X is observable and the predictor t is measured with additive error. The nonparametric function g(t) is estimated by the method of the smoothing spline. The parameters are given the prior by according to the Bayesian explanation of the smoothing spline and Bayesian linear regression. The parametric posterior distribution is sampled by the method of Gibbs sampling. The parameters are estimated by the posterior mean and the parametric posterior interval can constructed by the quantile of samples drew from the posterior distribution. The simulated example is used to illustrate our methodology.

Key words: smoothing spline, regression of errors-in-variable, Bayesian method, Gibbs sampling, MCMC simulation, partially linear model, smoothing spline, regression of errors-in-variable, Bayesian method, Gibbs sampling, MCMC simulation

中图分类号: