Adaptive confidence interval for pointwise curve estimation

Abstract

We present a procedure associated with nonlinear wavelet methods that provides adaptive confidence intervals around f(x0), 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.