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Honest confidence regions for nonparametric regression. (English) Zbl 0681.62047

Summary: The problem of constructing honest confidence regions for nonparametric regression is considered. A lower rate of convergence, \(n^{-1/4}\), for the size of the confidence region is established. The achievability of this rate is demonstrated using Stein’s estimates and the associated unbiased risk estimates. Practical implications are discussed.

MSC:

62G15 Nonparametric tolerance and confidence regions
62J99 Linear inference, regression
62G99 Nonparametric inference
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