Nonlinear and nonparametric regression and instrumental variables
Nonlinear and nonparametric regression and instrumental variables
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DOI：
10.1198/016214504000001088
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发表时间：
2004-09-01
影响因子：
3.7
通讯作者：
Karagas, MR
中科院分区：
文献类型：
--
作者：
Carroll, RJ;Ruppert, D;Karagas, MR
当有误差地测量预测值并且工具变量(TV)可用时，我们认为是回归。回归函数。或非参数。我们的主要新结果表明，回归函数和文中的所有参数都可以线性、非线性地建模。测量误差模型在相对较弱的条件下被辨识，比以前所知的意味着可辨识性的要弱得多。此外，我们利用IV估计器的特征作为一种经典的“衰减校正”方法，该方法基于测量误差的方差的特定估计。这种测量误差方差的估计允许我们构造泛函非参数回归估计，而不对未观察到的预测量的分布进行假设，以及使用关于该分布的参数假设的结构估计。函数估计采用模拟外推或反卷积核，结构方法采用贝叶斯马尔可夫链蒙特卡罗方法。研究发现，贝叶斯估计器的性能明显优于泛函方法。
We consider regression when the predictor is measured with error and an instrumental variable (TV) is available. The regression function., or nonparametrically. Our major new result shows that the regression function and all parameters in can be modeled linearly, nonlinearly the measurement error model are identified under relatively weak conditions, much weaker than previously known to imply identifiability. In addition, we exploit a characterization of the IV estimator as a classical "correction for attenuation" method based on a particular estimate of the variance of the measurement error. This estimate of the measurement error variance allows us to construct functional nonparametric regression estimators making no assumptions about the distribution of the unobserved predictor and structural estimators that use parametric assumptions about this distribution. The functional estimators uses, simulation extrapolation or deconvolution kernels and the structural method uses Bayesian Markov chain Monte Carlo. The Bayesian estimator is found to significantly outperform the functional approach.