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.
"Adaptive confidence interval for pointwise curve estimation." Ann. Statist. 28 (1) 298 - 335, February 2000. https://doi.org/10.1214/aos/1016120374