English

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}
}
R2 v1 2026-06-21T21:53:50.197Z