标题： 分布函数在测量误差模型中的估计 显示英文标题

标题： Estimation of distribution functions in measurement error models

摘要： 许多实际问题与当数据包含测量误差时分布函数的点估计有关。 这些问题的动机来自天文学、可靠性、质量控制、公共卫生和调查数据等多个领域。 最近，Dattner、Goldenshluger 和 Juditsky（2011）表明，当测量误差分布的特征函数尾部以多项式方式衰减时，基于分布函数直接反演公式的估计量具有良好的性质。 在本文中，我们推导了该估计量在误差分布更光滑情况下的理论性质，并研究了不同误差分布下的有限样本行为。 我们的方法是数据驱动的，因为我们仅使用已知的信息，即误差分布和数据。 还考察了该估计量在基于真实数据估计高血压患病率中的应用。 显示英文摘要

摘要： Many practical problems are related to the pointwise estimation of dis- tribution functions when data contains measurement errors. Motivation for these problems comes from diverse fields such as astronomy, reliability, quality control, public health and survey data. Recently, Dattner, Goldenshluger and Juditsky (2011) showed that an estimator based on a direct inversion formula for distribution functions has nice properties when the tail of the characteristic function of the mea- surement error distribution decays polynomially. In this paper we derive theoretical properties for this estimator for the case where the error distri- bution is smoother and study its finite sample behavior for different error distributions. Our method is data-driven in the sense that we use only known information, namely, the error distribution and the data. Applica- tion of the estimator to estimating hypertension prevalence based on real data is also examined.