论文标题
有条件密度估计与协变量误差
Conditional density estimation with covariate measurement error
论文作者
论文摘要
我们考虑在容易出错的协变量上估算响应条件的密度。在没有协变量测量误差的情况下，由两个现有的内核密度估计器激励，我们提出了一种纠正现有估计器的测量误差的方法。在不同类型的测量误差分布下，所得估计量的渐近特性得出了。此外，我们可以调整从现有的带宽选择方法可获得的带宽，以获取用于无错误数据的带宽，以获取新估计器的带宽。进行了广泛的仿真研究，以将提出的估计量与忽略测量误差的天真估计器进行比较，这也为提出的带宽选择方法的有效性提供了经验证据。现实生活中的数据示例用于说明在实际情况下实现这些方法。开发了一个R软件包LPME，用于实现所有考虑的方法，我们通过附录H中的R代码示例证明了这些方法。
We consider estimating the density of a response conditioning on an error-prone covariate. Motivated by two existing kernel density estimators in the absence of covariate measurement error, we propose a method to correct the existing estimators for measurement error. Asymptotic properties of the resultant estimators under different types of measurement error distributions are derived. Moreover, we adjust bandwidths readily available from existing bandwidth selection methods developed for error-free data to obtain bandwidths for the new estimators. Extensive simulation studies are carried out to compare the proposed estimators with naive estimators that ignore measurement error, which also provide empirical evidence for the effectiveness of the proposed bandwidth selection methods. A real-life data example is used to illustrate implementation of these methods under practical scenarios. An R package, lpme, is developed for implementing all considered methods, which we demonstrate via an R code example in Appendix H.
