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arXiv · 1709.07022

Anisotropic functional Fourier deconvolution with long-memory dependent errors: a minimax study

Rida Benhaddou
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Abstract

We investigate minimax results for the anisotropic functional deconvolution model when observations are affected by the presence of long-memory. Under specific conditions about the covariance matrices of the errors, we follow a standard procedure to construct an adaptive wavelet-based estimator that attains asymptotically near-optimal convergence rates. These rates depend on the parameter associated with the weakest long-range dependence, and deteriorate as the intensity of long-memory increases. This behavior suggests that the estimator adjusts to the best case scenario and that the weakest LM dominates.

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Rida Benhaddou. 2017-09-20. Anisotropic functional Fourier deconvolution with long-memory dependent errors: a minimax study. https://arxiv.org/abs/1709.07022

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