Asymptotic confidence sets for the jump curve in bivariate regression problems

JOURNAL OF MULTIVARIATE ANALYSIS

卷:173

Article

Bengs, Viktor¹  Eulert, Matthias¹  Holzmann, Hajo¹ 

[1] Philipps Univ Marburg, Math & Informat Fb 12, Hans Meerwein Str 6, D-35032 Marburg, Germany

关键词: Image processing;    Jump detection;    M-estimation;    Rotated difference kernel estimator;   

DOI  :  10.1016/j.jmva.2019.02.017

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free