Wavelet Shrinkage in Nonparametric Regression Models with Positive Noise

TL;DR

This paper develops Bayesian wavelet shrinkage methods tailored for nonparametric regression models with positive noise, addressing practical scenarios where noise is not Gaussian, and demonstrates their effectiveness through simulations and real data application.

Contribution

It introduces novel Bayesian shrinkage rules for wavelet coefficients in models with positive noise, expanding beyond traditional Gaussian assumptions.

Findings

Proposed shrinkage rules outperform standard techniques in simulations.

Methods effectively handle exponential and lognormal noise distributions.

Application to Boston Marathon data illustrates practical utility.

Abstract

Wavelet shrinkage estimators are widely applied in several fields of science for denoising data in wavelet domain by reducing the magnitudes of empirical coefficients. In nonparametric regression problem, most of the shrinkage rules are derived from models composed by an unknown function with additive gaussian noise. Although gaussian noise assumption is reasonable in several real data analysis, mainly for large sample sizes, it is not general. Contaminated data with positive noise can occur in practice and nonparametric regression models with positive noise bring challenges in wavelet shrinkage point of view. This work develops bayesian shrinkage rules to estimate wavelet coefficients from a nonparametric regression framework with additive and strictly positive noise under exponential and lognormal distributions. Computational aspects are discussed and simulation studies to analyse the performances of the proposed shrinkage rules and compare them with standard techniques are done. An application in winning times Boston Marathon dataset is also provided.