 Asymptotic confidence sets for the jump curve in bivariate regression problemsViktor Bengs, Matthias Eulert and Hajo Holzmann Journal of Multivariate Analysis, 2019, vol. 173, issue C, 291-312 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. Keywords: Image processing; Jump detection; M-estimation; Rotated difference kernel estimator (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:173:y:2019:i:c:p:291-312 Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2019.02.017 Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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