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Wavelet deconvolution in a periodic setting with long-range dependent errors. (English) Zbl 1259.62075

Summary: A hard thresholding wavelet estimator is constructed for a deconvolution model in a periodic setting that has long-range dependent (LRD) noise. The estimation paradigm is based on a maxiset method that attains a near optimal rate of convergence for a variety of \(\mathcal L_{p}\) 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 \(\mathsf{WaveD}\)-package in \(\mathsf{R}\) 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 \(\mathsf{WaveD}\) approach.

MSC:

62M09 Non-Markovian processes: estimation
65T60 Numerical methods for wavelets
62G05 Nonparametric estimation
65C60 Computational problems in statistics (MSC2010)
62G07 Density estimation

Software:

R; longmemo; WaveD
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Full Text: DOI arXiv

References:

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