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Empirical likelihood confidence intervals for local linear smoothers. (English) Zbl 1028.62034

Summary: Empirical likelihood is considered in conjunction with the local linear smoother to construct confidence intervals for a nonparametric regression function with bounded support. The coverage error of the empirical likelihood confidence intervals is evaluated and is shown to be of the same order throughout the support of the regression function. This is a significant improvement over confidence intervals based directly on the asymptotic normal distribution of the local linear estimator, which have a larger order of coverage error near the boundary. This improvement is attributable to the natural variance estimator that empirical likelihood implicitly chooses for the local linear smoother.

MSC:

62G15 Nonparametric tolerance and confidence regions
62G08 Nonparametric regression and quantile regression
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