The graphical advantages of finite interval confidence band procedures

Abstract

When presented as graphical illustrations, regression surface confidence bands for linear statistical models quickly convey detailed information about analysis results. A taut confidence band is a compact set of curves which are estimation candidates for the unobservable, fixed regression curve. The bounds of the band are usually plotted with the estimated regression curve and may be overlaid by a scatter-plot of the data to provide an integrated visual impression. Finite-interval confidence bands offer the advantages of clearer interpretation and improved efficiency and avoid visual ambiguities inherent to infinite-interval bands. The definitive characteristic of a finite-interval confidence band is that it is only necessary to plot it over a finite interval in order to visually communicate all its information. In contrast, visual representations of infinite-interval bands are not fully informative and can be misleading. When an infinite-interval band is plotted, and therefore truncated, substantial information given by its asymptotic behavior is lost. Many curves that are clearly within the plotted portion of the infinite interval confidence band eventually cross a boundary. In practice, a finite-interval band can always be easily obtained from any infinite-interval band. This article focuses on interpretational considerations of symmetric confidence bands as graphical devices.

Keywords:

• Graphical methods
• Simultaneous statistical inference