WIAS Preprint No. 34, (1992)

Pointwise confidence intervals in nonparametric regression with heteroscedastic error structure.


  • Neumann, Michael H.

2010 Mathematics Subject Classification

  • 62G15 62G07 62E20


  • Nonparametric regression, asymptotic confidence interval, error in coverage probability, Edgeworth expansion, wild bootstrap




We assume a nonparametric model with heteroscedastic error structure and consider pointwise confidence intervals for the mean. We construct confidence intervals by using quantiles from a Cornish-Fisher expansion and from the wild bootstrap distribution, with as well as without a subsequent bias correction. It turns out that pure undersmoothing, where the full smoothness is used by the initial estimator, outperforms the method with a subsequent bias correction.

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