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Asymptotic confidence sets for the jump curve in bivariate regression problems

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  • Bengs, Viktor
  • Eulert, Matthias
  • Holzmann, Hajo

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.

Suggested Citation

  • Bengs, Viktor & Eulert, Matthias & Holzmann, Hajo, 2019. "Asymptotic confidence sets for the jump curve in bivariate regression problems," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 291-312.
    • Handle: RePEc:eee:jmvana:v:173:y:2019:i:c:p:291-312
    DOI: 10.1016/j.jmva.2019.02.017
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    References listed on IDEAS

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    5. Mammen, Enno & Polonik, Wolfgang, 2013. "Confidence regions for level sets," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 202-214.
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