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Adaptive confidence interval for pointwise curve estimation. (English) Zbl 1106.62331

Summary: We present a procedure associated with nonlinear wavelet methods that provides adaptive confidence intervals around \(f(x_0)\), in either a white noise model or a regression setting. A suitable modification in the truncation rule for wavelets allows construction of confidence intervals that achieve optimal coverage accuracy up to a logarithmic factor. The procedure does not require knowledge of the regularity of the unknown function \(f\); it is also efficient for functions with a low degree of regularity.

MSC:

62G15 Nonparametric tolerance and confidence regions
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
62G07 Density estimation
62G08 Nonparametric regression and quantile regression
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