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Alternative Title
Abstract
Point-wise confidence intervals for a non-parametric regression function in conjunction with the popular local linear smoother are considered. The confidence intervals are based on the asymptotic normal distribution of the local linear smoother. Their coverage accuracy is evaluated by developing Edgeworth expansion for the coverage probability. It is found that the coverage error near the boundary of the support of the regression function is of a larger order than that in the interior, which implies that the local linear smoother is not adaptive to the boundary in terms of coverage. This is quite unexpected as the local linear smoother is adaptive to the boundary in terms of the mean squared error.
Keywords
Confidence interval, Coverage probability, Edgeworth expansion, Non-parametric regression, Normal approximation
Source Title
Scandinavian Journal of Statistics
Publisher
Series/Report No.
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Date
2002-03
DOI
10.1111/1467-9469.00028
Type
Article