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Confidence sets for change-point problems in nonparametric regression
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...
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| Formaat: | Dissertation |
| Taal: | Engels |
| Gepubliceerd in: |
Philipps-Universität Marburg
2018
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| Onderwerpen: | |
| Online toegang: | PDF Full text |
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| Samenvatting: | 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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| Fysieke beschrijving: | 171 Seiten |
| DOI: | 10.17192/z2018.0511 |