Minimax theory for a class of non-linear statistical inverse problems
Statistics Theory
2016-11-08 v2 Methodology
Statistics Theory
Abstract
We study a class of statistical inverse problems with non-linear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the non-linearity. This reduces the initial non-linear problem to a linear inverse problem with deterministic noise, which is then solved in a second step. The noise reduction step is based on wavelet thresholding and is shown to be minimax optimal (up to logarithmic factors) in a pointwise function-dependent sense. Our analysis is based on a modified notion of H\"older smoothness scales that are natural in this setting.
Cite
@article{arxiv.1512.00218,
title = {Minimax theory for a class of non-linear statistical inverse problems},
author = {Kolyan Ray and Johannes Schmidt-Hieber},
journal= {arXiv preprint arXiv:1512.00218},
year = {2016}
}
Comments
37 pages