Cross-Validated Wavelet Block Thresholding for Non-Gaussian Errors

TL;DR

This paper introduces a distribution-free wavelet thresholding method for nonparametric regression with non-normal errors, improving accuracy through cross-validation, block thresholding, and level dependence, validated on simulated and real data.

Contribution

It proposes a novel, distribution-free wavelet thresholding approach that does not require knowing the error distribution, enhancing non-normal error handling in nonparametric regression.

Findings

Effective on various non-normal error distributions

Outperforms existing wavelet threshold estimators

Validated on simulated and real datasets

Abstract

Wavelet thresholding generally assumes independent, identically distributed normal errors when estimating functions in a nonparametric regression setting. VisuShrink and SureShrink are just two of the many common thresholding methods based on this assumption. When the errors are not normally distributed, however, few methods have been proposed. A distribution-free method for thresholding wavelet coefficients in nonparametric regression is described, which unlike some other non-normal error thresholding methods, does not assume the form of the non-normal distribution is known. Improvements are made to an existing even-odd cross-validation method by employing block thresholding and level dependence. The efficiency of the proposed method on a variety of non-normal errors, including comparisons to existing wavelet threshold estimators, is shown on both simulated and real data.