- Thesis:
- Bachelor in Mathematics
- Author:
- Fabia Martens
- Title:
- Modellauswahl und Bernstein Ungleichungen für Suprema von Zufallsprozessen
- Supervisor:
- Jan JOHANNES
- Abstract:
- We consider the regression framework: Y=f+e where f = (f1,..,fn) is an unknown vector in Rn and e = (e1,..,en) is a random vector, the components of which are independent, centered and admit finite Laplace transforms a neighborhood of 0. Our aim is to estimate f from the observation of Y. The first part of this thesis oriented towards the function f. We assume here an oracle-type inequality, which optimizes our estimator. The second part orients towards the control of this estimator through a penalty criterion. First we are observing the error term and then we observe the whole estimator through histogramms.
References:- Y. Baraud. A Bernstein-type inequality for suprema of random processes with applications to model selection in non-Gaussian regression, Bernoulli, 16(4):1064–1085, 2010.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |