Many nonparametric regression estimators (smoothers) have been proposed that provide a more flexible method for estimating the true regression line compared to using some of the more obvious parametric models. A basic goal when using any smoother is computing a confidence band for the true regression line. Let M(Y|X) be some conditional measure of location associated with the random variable Y, given X and let x be some specific value of the covariate. When using the LOWESS estimator, an extant method that assumes homoscedasticity can be used to compute a confidence interval for M(Y|X = x). A trivial way of computing a confidence band is to compute confidence intervals for K covariate values, each having probability coverage 1 − α. But an obvious concern is that the simultaneous probability coverage can be substantially smaller than 1 − α. A method is suggested for dealing with this issue that allows heteroscedasticity and simultaneously performs better than the Bonferroni method or the Studentized maximum modulus distribution.
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机译：提出了许多非参数回归估计器（平滑器），与使用某些更明显的参数模型相比，它们提供了一种更灵活的方法来估计真实回归线。使用任何平滑器的基本目标是计算真实回归线的置信带。在给定X的情况下，令M（Y | X）是与随机变量Y相关的位置的某些条件度量，而x是协变量的某些特定值。当使用LOWESS估计器时，可以使用假定同调的现存方法来计算M（Y | X = x）的置信区间。计算置信带的一种简单方法是计算K个协变量值的置信区间，每个协变量值的概率覆盖范围为1-α。但一个明显的担忧是，同时概率覆盖范围可能大大小于1-α。建议一种用于解决此问题的方法，该方法允许异方差性，并且同时比Bonferroni方法或Studentized最大模量分布更好。
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