论文标题
固定设计下的伯克森错误回归的同时推断伯克森错误回归
Simultaneous inference for Berkson errors-in-variables regression under fixed design
论文作者
论文摘要
在回归分析的各种应用中，除了相关观测值的错误外，预测变量中的错误还起着重要作用，需要将其纳入统计建模过程中。在本文中，我们考虑了带有固定设计回归器和居中随机误差的伯克森类型的非参数测量误差模型，这与许多现有工作相反，在这些工作中，预测因子被视为具有随机噪声的随机观察。基于将预测器中的误差考虑到合适的高斯近似值的估计器，我们为感兴趣的功能得出了％均匀的置信声。特别是，我们在统一置信带的覆盖误差上提供了有限的样本界限，在这里我们规避了极端价值理论的使用，而不是依靠最新结果对高斯过程的抗浓缩。在一项模拟研究中，我们研究了有限样品的均匀置信度集的性能。
In various applications of regression analysis, in addition to errors in the dependent observations also errors in the predictor variables play a substantial role and need to be incorporated in the statistical modeling process. In this paper we consider a nonparametric measurement error model of Berkson type with fixed design regressors and centered random errors, which is in contrast to much existing work in which the predictors are taken as random observations with random noise. Based on an estimator that takes the error in the predictor into account and on a suitable Gaussian approximation, we derive %uniform confidence statements for the function of interest. In particular, we provide finite sample bounds on the coverage error of uniform confidence bands, where we circumvent the use of extreme-value theory and rather rely on recent results on anti-concentration of Gaussian processes. In a simulation study we investigate the performance of the uniform confidence sets for finite samples.
