Wavelet Deconvolution in a Periodic Setting with Long-Range Dependent Errors
Methodology
2015-03-20 v1
Abstract
In this paper, a hard thresholding wavelet estimator is constructed for a deconvolution model in a periodic setting that has long-range dependent noise. The estimation paradigm is based on a maxiset method that attains a near optimal rate of convergence for a variety of L_p loss functions and a wide variety of Besov spaces in the presence of strong dependence. The effect of long-range dependence is detrimental to the rate of convergence. The method is implemented using a modification of the WaveD-package in R and an extensive numerical study is conducted. The numerical study supplements the theoretical results and compares the LRD estimator with na\"ively using the standard WaveD approach.
Keywords
Cite
@article{arxiv.1208.4441,
title = {Wavelet Deconvolution in a Periodic Setting with Long-Range Dependent Errors},
author = {Justin Rory Wishart},
journal= {arXiv preprint arXiv:1208.4441},
year = {2015}
}