Dokument
| Titel: | Confidence sets for change-point problems in nonparametric regression |
| Autor: | Bengs,Viktor |
| Weitere Beteiligte: | Holzmann, Hajo (Prof. Dr.) |
| Veröffentlicht: | 2018 |
| URI: | https://archiv.ub.uni-marburg.de/diss/z2018/0511 |
| DOI: | https://doi.org/10.17192/z2018.0511 |
| URN: | urn:nbn:de:hebis:04-z2018-05119 |
| DDC: | 510 Mathematik |
| Titel (trans.): | Konfidenzmengen für nichtparametrische Regressionsproblemen mit Sprüngen |
| Publikationsdatum: | 2019-04-24 |
| Lizenz: | https://rightsstatements.org/vocab/InC-NC/1.0/ |
| Schlagwörter: |
|---|
| image processing, Lepski’s method, confidence bands, change-point estimation, jump detection, nonpa, M-Estimation, limit theorems, Adaptive estimation |
Summary:
In this thesis, confidence sets for different nonparametric regression problems with change-points are developed. Uniform and pointwise asymptotic confidence bands for the jump-location-curve in a boundary fragment model using methods from M-estimation and Gaussian approximation are constructed for the rotated difference kernel estimator. In addition, estimation of the location and of the height of the jump in some derivative of a regression curve is considered. Optimal convergence rates as well as the joint asymptotic normal distribution of estimators based on the zero-crossing-time technique are established over certain Hölder-classes. Further, joint as well as marginal asymptotic confidence sets which are honest and adaptive for these parameters over specific Hölder-classes are constructed. The finite-sample performance is investigated in simulation studies, and real data illustrations are given.
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