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Standard approaches to constructing nonparametric confidence bands forfunctions are frustrated by the impact of bias, which generally is notestimated consistently when using the bootstrap and conventionally smoothedfunction estimators. To overcome this problem it is common practice to eitherundersmooth, so as to reduce the impact of bias, or oversmooth, and therebyintroduce an explicit or implicit bias estimator. However, these approaches,and others based on nonstandard smoothing methods, complicate the process ofinference, for example, by requiring the choice of new, unconventionalsmoothing parameters and, in the case of undersmoothing, producing relativelywide bands. In this paper we suggest a new approach, which exploits to ouradvantage one of the difficulties that, in the past, has prevented anattractive solution to the problem - the fact that the standard bootstrap biasestimator suffers from relatively high-frequency stochastic error. The highfrequency, together with a technique based on quantiles, can be exploited todampen down the stochastic error term, leading to relatively narrow,simple-to-construct confidence bands.

A simple bootstrap method for constructing nonparametric confidence bands for functions