2005: Bootstrapping Simultaneous Confidence Bands

Once a regression has been fitted to data, it is usually necessary to add confidence intervals to indicate the accuracy of the fitted regression line. This can easily be done for individual explanatory variable values. However sometimes confidence limits are needed simultaneously for the whole range of explanatory variable values of interest. In other words the problem is to construct a confidence band within which the entire unknown true regression line lies with given confidence. This article discusses computer intensive methods for doing this. The advantage of such methods compared with classical asymptotic methods is that accurate coverages can be obtained quite easily using bootstrap resampling.