Anisotropic functional Fourier deconvolution with long-memory dependent errors: a minimax study
Statistics Theory
2018-07-31 v2 Statistics Theory
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.
Cite
@article{arxiv.1709.07022,
title = {Anisotropic functional Fourier deconvolution with long-memory dependent errors: a minimax study},
author = {Rida Benhaddou},
journal= {arXiv preprint arXiv:1709.07022},
year = {2018}
}