Asymptotic confidence sets for the jump curve in bivariate regression problems
Abstract
We construct uniform and point-wise asymptotic confidence sets for the single edge in an otherwise smooth image function which are based on rotated differences of two one-sided kernel estimators. Using methods from M-estimation, we show consistency of the estimators of location, slope and height of the edge function and develop a uniform linearization of the contrast process. The uniform confidence bands then rely on a Gaussian approximation of the score process together with anti-concentration results for suprema of Gaussian processes, while point-wise bands are based on asymptotic normality. The finite-sample performance of the point-wise proposed methods is investigated in a simulation study. An illustration to real-world image processing is also given.
Cite
@article{arxiv.1903.09859,
title = {Asymptotic confidence sets for the jump curve in bivariate regression problems},
author = {Viktor Bengs and Matthias Eulert and Hajo Holzmann},
journal= {arXiv preprint arXiv:1903.09859},
year = {2019}
}