Wavelet shrinkage in nonparametric regression models with positive noise

Abstract

ABSTRACT Wavelet shrinkage estimators are widely applied to analyse datasets in wavelet domain from several fields of science. They typically act by reducing magnitudes of empirical coefficients in a discrete wavelet transformation to estimate wavelet coefficients. In nonparametric regression problems, most of the shrinkage rules are derived from models composed of 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. In this sense, this work proposes 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 for winning times Boston Marathon dataset is also provided.