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.
Wilcox, R. (2017). The Regression Smoother LOWESS: A Confidence Band That Allows Heteroscedasticity And Has Some Specified Simultaneous Probability Coverage. Journal of Modern Applied Statistical Methods, 16(2), 29-38. doi: 10.22237/jmasm/1509494580