SIMEX and standard error estimation in semiparametric measurement error models.
SIMEX and standard error estimation in semiparametric measurement error models.
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DOI：
10.1214/08-ejs341
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发表时间：
2009-01-01
影响因子：
1.1
通讯作者：
Maity A
中科院分区：
文献类型：
--
作者：
Apanasovich TV;Carroll RJ;Maity A
SIMEX是一种用于测量误差校正的通用技术。有大量文献的应用和理论的SIMEX纯参数问题，以及纯非参数回归问题，但既没有应用程序，也没有理论的半参数问题。受辐射剂量学的一个例子的启发，我们开发了半参数问题的SIMEX的基本理论，使用基于核的估计方法。这包括被误测的变量被完全参数化建模、完全非参数化建模、或者被误测的变量具有被参数化建模和非参数化建模的分量的情况。使用我们的渐近展开式，容易计算的标准误差公式推导，是非参数估计的偏差性质。标准误差方法是一种新的方法，估计变异性的非参数估计在半参数问题，我们在模拟和我们的例子中，它显着提高了一阶方法。我们发现，为了估计模型的参数部分，O（n−1/5）阶的标准带宽选择足以确保渐近正态性，并且不需要欠平滑。SIMEX具有适合错误指定的模型的特性，即忽略测量误差的模型。因此，我们的工作也更一般地描述了基于核的方法在错误指定的半参数问题的行为。
SIMEX is a general-purpose technique for measurement error correction. There is a substantial literature on the application and theory of SIMEX for purely parametric problems, as well as for purely non-parametric regression problems, but there is neither application nor theory for semiparametric problems. Motivated by an example involving radiation dosimetry, we develop the basic theory for SIMEX in semiparametric problems using kernel-based estimation methods. This includes situations that the mismeasured variable is modeled purely parametrically, purely non-parametrically, or that the mismeasured variable has components that are modeled both parametrically and nonparametrically. Using our asymptotic expansions, easily computed standard error formulae are derived, as are the bias properties of the nonparametric estimator. The standard error method represents a new method for estimating variability of nonparametric estimators in semiparametric problems, and we show in both simulations and in our example that it improves dramatically on first order methods. We find that for estimating the parametric part of the model, standard bandwidth choices of order O(n−1/5) are sufficient to ensure asymptotic normality, and undersmoothing is not required. SIMEX has the property that it fits misspecified models, namely ones that ignore the measurement error. Our work thus also more generally describes the behavior of kernel-based methods in misspecified semiparametric problems.