- Thesis:
- Bachelor in Mathematics
- Author:
- Joanna Schnorr
- Title:
- Variable selection with Hamming loss
- Supervisor:
- Jan JOHANNES
- Abstract:
- In this thesis, we study estimators that select relevant components of a d- dimensional, real-valued vector that has at most s nonzero components, and these com- ponents are separated from zero at least by a constant a. We consider a Gaussian sequence model and compare the risk of each selector to the minimax risk under Hamming loss. In a special case, we find a minimax selector. Then we extend these results to dependent observations and non-Gaussian models. In an asymptotic analysis we find conditions such that exact and almost full recovery are achieved. Furthermore, we consider adaptive selectors that do not depend on s and a. Finally, we illustrate some of the results in a numerical study.
References:- C. Butucea, M. Ndaoud, N. Stepanova, and A.B. Tsybakov. Variable selection with Hamming loss, The Annals of Statistics, 46(5):1837-1875, 2018.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |