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arXiv · 1208.4441

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

Justin Rory Wishart
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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 naïvely using the standard WaveD approach.

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Justin Rory Wishart. 2012-08-22. Wavelet Deconvolution in a Periodic Setting with Long-Range Dependent Errors. https://arxiv.org/abs/1208.4441

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