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