Confidence sets for change-point problems in nonparametric regression

Bengs, Viktor (2018): Confidence sets for change-point problems in nonparametric regression. Dissertation, Philipps-Universität Marburg

Abstract

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.

• Item Type: Thesis (Dissertation)
• Faculties: Mathematics, Computer Science and Statistics > Computer Science > Artificial Intelligence and Machine Learning
• Subjects: 000 Computer science, information and general works > 004 Data processing computer science
• Language: English