Robustness of Tube Formula Based Confidence Bands
研究了管公式在非高斯误差下构造回归曲线同时置信带的稳健性，发现球对称分布下公式不变，模拟显示对污染和厚尾误差可接受，但离散和高度偏斜误差下可能失效。
Abstract Simultaneous confidence bands of a regression curve may be used to quantify the uncertainty of an estimate of the curve. The tube formula for volumes of tubular neighborhoods of a manifold provides a very powerful 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 error vector with a spherically symmetric distribution. Simulations are used for a variety of independent non-Gaussian error distributions. The results are acceptable for contaminated and heavy tailed error distributions. The formula can break down in some extreme cases for discrete and highly skewed errors. Computational issues involved in applying the tube formula are also discussed. Key Words: RegressionSimultaneous inferenceTail probability