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Bootstrap confidence bands for regression curves and their derivatives. (English) Zbl 1042.62044

Summary: Confidence bands for regression curves and their first \(p\) derivatives are obtained via local \(p\) th-order polynomial estimation. The method allows for multiparameter local likelihood estimation as well as other unbiased estimating equations. As an alternative to the confidence bands obtained by asymptotic distribution theory, we also study smoothed bootstrap confidence bands. Simulations illustrate the finite sample properties of the methodology.

MSC:

62G15 Nonparametric tolerance and confidence regions
62G09 Nonparametric statistical resampling methods
62G08 Nonparametric regression and quantile regression
62E20 Asymptotic distribution theory in statistics
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