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Wavelet Deconvolution in a Periodic Setting with Long-Range Dependent Errors

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 naïvely using the standard WaveD approach.

preprint2012arXivOpen access
Justin Rory Wishart
Methodology
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Justin Rory Wishart

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