Dilation-Invariant Wavelet Estimation

Abstract

A wavelet method is proposed that reduces function estimation error and provides smooth reconstructions, while still estimating jumps in the function well. It is based on analyzing multiple dilated versions of the sampled function. In simulation studies, the estimator exhibits low mean squared errors without sacrificing smoothness or jump detection ability when compared to other wavelet methods.

Keywords:

• Nonparametric regression
• Thresholding
• Translation-invariant
• Wavelets

Mathematics Subject Classification:

• 42C40
• 62G08