ROBUSTNESS OF TUBE FORMULA BASED CONFIDENCE BANDS

Simultaneous confidence bands of a regression curve may be used to qua ntify the uncertainty of an estimate of the curve. The tube formula fo r volumes of tubular neighborhoods of a manifold provides a very power ful method for obtaining such bands at a prescribed level, when errors are Gaussian. This article studies robustness of the tube formula for non-Gaussian errors. The formula holds without modification for an er ror vector with a spherically symmetric distribution. Simulations are used for a variety of independent non-Gaussian error distributions. Th e results an acceptable for contaminated and heavy tailed error distri butions. The formula can break down in some extreme casts for discrete and highly skewed errors. Computational issues involved in applying t he tube formula are also discussed.