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 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.

在回归分析的各种应用中，除了依赖观察中的误差外，预测变量中的误差也起着重要作用，需要纳入统计建模过程。在本文中，我们考虑了一个 Berkson 类型的非参数测量误差模型，该模型具有固定的设计回归量和中心随机误差，这与许多现有的工作形成对比，在这些工作中，预测变量被视为具有随机噪声的随机观测值。基于将预测器中的误差考虑在内的估计器和合适的高斯近似，我们推导了统一置信带覆盖误差的有限样本界限，其中我们规避​​了极值理论的使用，而是依赖于最近的结果关于高斯过程的反集中。