Wavelet deconvolution in a periodic setting with long-range dependent errors

Justin Rory Wishart*

*Corresponding author for this work

Research output: Contribution to journalArticle

10 Citations (Scopus)

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 Lp 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 a naïve application of the standard WaveD approach.

Original languageEnglish
Pages (from-to)867-881
Number of pages15
JournalJournal of Statistical Planning and Inference
Volume143
Issue number5
DOIs
Publication statusPublished - May 2013
Externally publishedYes

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