  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.
