Simultaneous confidence bands for a percentile line in linear regression

Construction of simultaneous confidence bands for a percentile line in linear regression has been considered by several authors. But only conservative symmetric bands, which use critical constants over the whole covariate range (−∞,∞), are available in the literature. New methods allow the construction of exact symmetric bands for a percentile line over a finite interval of the covariate x. The exact symmetric bands can be substantially narrower than the corresponding conservative symmetric bands. Several exact symmetric confidence bands are compared under the average band width criterion. Furthermore, new asymmetric confidence bands for a percentile line are proposed. They are uniformly and can be very substantially narrower than the corresponding exact symmetric bands. Therefore, asymmetric bands should always be used under the average band width criterion. The proposed methods are illustrated with a real example.