Nonparametric regression estimation in the heteroscedastic errors-in-variables problem
Nonparametric regression estimation in the heteroscedastic errors-in-variables problem
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DOI：
10.1198/016214507000000987
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发表时间：
2007-12-01
影响因子：
3.7
通讯作者：
Meister, Alexander
中科院分区：
文献类型：
--
作者：
Delaigle, Aurore;Meister, Alexander
在经典的变量误差问题中，目标是从数据中估计回归曲线，其中解释变量是有误差的。在这种情况下，非参数方法已被提出，依赖于假设的测量误差是相同的分布。虽然有很多情况下，这种假设是过于严格，在更现实的异方差误差设置的非参数估计还没有在文献中研究。我们提出了一个估计的回归函数在这样的设置，并表明它是最佳的。我们估计的情况下，误差分布是未知的和复制的意见。实用的方法，包括自适应带宽选择器的误差变量回归问题，建议，并通过模拟和真实的数据的例子说明其有限样本性能。
In the classical errors-in-variables problem, the goal is to estimate a regression curve from data in which the explanatory variable is measured with error. In this context, nonparametric methods have been proposed that rely on the assumption that the measurement errors are identically distributed. Although there are many situations in which this assumption is too restrictive, nonparametric estimators in the more realistic setting of heteroscedastic errors have not been studied in the literature. We propose an estimator of the regression function in such a setting and show that it is optimal. We give estimators in cases in which the error distributions are unknown and replicated observations are available. Practical methods, including an adaptive bandwidth selector for the errors-in-variables regression problem, are suggested, and their finite-sample performance is illustrated through simulated and real data examples.