Wang Huixia Judy, Stefanski Leonard A, Zhu Zhongyi
Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, U.S.A. ,
Biometrika. 2012 Jun;99(2):405-421. doi: 10.1093/biomet/ass005. Epub 2012 Mar 30.
We study estimation in quantile regression when covariates are measured with errors. Existing methods require stringent assumptions, such as spherically symmetric joint distribution of the regression and measurement error variables, or linearity of all quantile functions, which restrict model flexibility and complicate computation. In this paper, we develop a new estimation approach based on corrected scores to account for a class of covariate measurement errors in quantile regression. The proposed method is simple to implement. Its validity requires only linearity of the particular quantile function of interest, and it requires no parametric assumptions on the regression error distributions. Finite-sample results demonstrate that the proposed estimators are more efficient than the existing methods in various models considered.
我们研究了协变量存在测量误差时的分位数回归估计问题。现有方法需要严格的假设，比如回归变量和测量误差变量的联合分布为球对称，或者所有分位数函数为线性，这些假设限制了模型的灵活性并使计算复杂化。在本文中，我们基于校正得分开发了一种新的估计方法，以处理分位数回归中的一类协变量测量误差。所提出的方法易于实现。其有效性仅要求感兴趣的特定分位数函数为线性，并且对回归误差分布无需参数假设。有限样本结果表明，在所考虑的各种模型中，所提出的估计量比现有方法更有效。
