Simultaneous bootstrap confidence bands in nonparametric regression

Abstract

In the present paper we construct asymptotic confidence bands in non-parametric regression. Our assumptions cover unequal variances of the observations and nonuni-form, possibly considerably clustered design. The confidence band is based on an undersmoothed local polynomial estimator. An appropriate quantile is obtained via the wild bootstrap. We derive certain rates (in the sample size n) for the error in coverage probability, which improves on existing results for methods that rely on the asymptotic distribution of the maximum of some Gaussian process. We propose a practicable rule for a data-dependent choice of the band-width. A small simulation study illustrates the possible gains by our approach over alternative frequently used methods.

Keywords:

• Nonparametric regression
• confidence bands
• bootstrap
• local polynomial estimator
• strong approximation

1991 Mathematics Subject Classification:

• Primary: 62607
• Secondary: 62609
• 62615