In two sample problems it is of interest to examine the difference between the two regression curves or to detect whether certain functions are adequate to describe the overall trend of the difference. In this paper, we propose a simultaneous confidence band (SCB) as a global inference method with asymptotically correct coverage probabilities for the difference curve based on the weighted local linear kernel regression estimates in each sample. Our procedure allows for random designs, different sample sizes, heteroscedastic errors, and especially missing covariates. Simulation studies are conducted to investigate the finite sample properties of the new SCB which support our asymptotic theory. The proposed SCB is used to analyze two data sets, one of which is concerned with human event-related potentials data which are fully observed and the other is concerned with the Canada 2010/2011 youth student survey data with partially missing covariates, leading to a number of discoveries.

中文翻译：

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两个回归平均曲线之间差异的全局统计推断，协变量可能部分缺失

在两个样本问题中，检查两条回归曲线之间的差异或检测某些函数是否足以描述差异的总体趋势是有意义的。在本文中，我们提出了一种同时置信带 (SCB) 作为全局推理方法，基于每个样本中的加权局部线性核回归估计，对差异曲线具有渐近正确的覆盖概率。我们的程序允许随机设计、不同的样本量、异方差误差，尤其是缺失的协变量。进行模拟研究以研究支持我们渐近理论的新 SCB 的有限样本特性。建议的 SCB 用于分析两个数据集，