- Thesis:
- Bachelor in Mathematics
- Author:
- Amelia Faber
- Title:
- Gaussian mean estimation and model selection without known variance
- Supervisor:
- Jan JOHANNES
- Abstract:
- In this thesis, we consider the problem of estimating the mean vector μ of a Gaussian vector Y ∈ Rn, whose components are independent and share a common, unknown variance. The estimation is performed via model selection over a countable collection of linear subspaces S of Rn, based on a penalized criterion. Our first objective is to derive a general upper bound on the risk E[∥μ − μˆmˆ ∥2], valid for any such collection and any non-negative penalty function. Building on this result, we propose a new penalty structure that balances model complexity and overfitting. We analyze both its theoretical guarantees and practical performance. As a central application, we study the problem of detecting nonzero mean components in a sparse high-dimensional setting and validate our approach through a detailed simulation study.
References:- Y. Baraud, C. Giraud, und Sylvie Huet. _Gaussian model selection with an unknown Variance, The Annals of Statistics 37(2):630–672, 2009.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |