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Sharp Confidence Bands for Percentile Lines and Tolerance Bands for the Simple Linear Model

简单线性模型百分位数曲线的紧置信带与容忍带

This article develops sharp confidence bands for percentiles of regression functions over finite intervals. Attention is focused on one-sided (upper) bands for these percentiles, but a simple extension allows construction of two-sided bands. These upper bands are useful for tolerance bands, since a 100-γ percent confidence band for the 100/βth percentile is also a γ coefficient β-tolerance band.

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Simultaneous Confidence Bands for Percentile Lines in the General Linear Model

一般线性模型中百分位数线的同时置信带

This article is a generalization of the procedures developed by Steinhorst and Bowden (1971) for constructing confidence bands for the 100βth percentiles in the general linear model. Since the original procedure built these bands about a biased estimator of the 100βth precentile line, some other estimators were tried. While some improvement was noted, the results are not conclusive, suggesting that the best procedure has not been found yet.

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