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Wavelet shrinkage estimators are widely applied in several fields of sciencefor denoising data in wavelet domain by reducing the magnitudes of empiricalcoefficients. In nonparametric regression problem, most of the shrinkage rulesare derived from models composed by an unknown function with additive gaussiannoise. Although gaussian noise assumption is reasonable in several real dataanalysis, mainly for large sample sizes, it is not general. Contaminated datawith positive noise can occur in practice and nonparametric regression modelswith positive noise bring challenges in wavelet shrinkage point of view. Thiswork develops bayesian shrinkage rules to estimate wavelet coefficients from anonparametric regression framework with additive and strictly positive noiseunder exponential and lognormal distributions. Computational aspects arediscussed and simulation studies to analyse the performances of the proposedshrinkage rules and compare them with standard techniques are done. Anapplication in winning times Boston Marathon dataset is also provided.

Wavelet Shrinkage in Nonparametric Regression Models with Positive Noise