Journal of Statistics: Advances in Theory and ApplicationsAuthor's: Alex Rodrigo Dos S. Sousa
Pages: [13] - [44]
Received Date: October 27, 2021; Revised November 9, 2021
Submitted by:
DOI: http://dx.doi.org/10.18642/jsata_7100122240
Shrinkage estimators are usually applied to estimate wavelet coefficients by reducing the magnitudes of wavelet empirical coefficients in nonparametric regression modelling. There are several well succeeded available wavelet shrinkage estimators in the literature, but most of them work under the assumption of Gaussian noise in the original data. Although Gaussian noise might be observed in practice and allows several good estimation properties, it is not a general case. One might have data with additive non-gaussian noise and, specifically for this work, strictly positive noise. This paper evaluates the performance of standard wavelet shrinkage estimators in denoising data under positive noise by the conduction of simulation studies involving the so called Donoho and Johnstone test functions. It was observed good performances of bayesian shrinkage rules in terms of averaged mean squared and averaged median absolute errors measures.
positive noise, wavelet shrinkage, nonparametric regression.
