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arXiv · 1903.09859

Asymptotic confidence sets for the jump curve in bivariate regression problems

Viktor Bengs·Matthias Eulert·Hajo Holzmann
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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.

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Viktor Bengs, Matthias Eulert, Hajo Holzmann. 2019-03-23. Asymptotic confidence sets for the jump curve in bivariate regression problems. https://doi.org/10.1016/j.jmva.2019.02.017

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