Dokument
| Titel: | High-dimensional, robust, heteroscedastic variable selection with the adaptive LASSO, and applications to random coefficient regression |
| Autor: | Hermann, Philipp |
| Weitere Beteiligte: | Holzmann, Hajo (Prof. Dr.) |
| Veröffentlicht: | 2021 |
| URI: | https://archiv.ub.uni-marburg.de/diss/z2021/0248 |
| DOI: | https://doi.org/10.17192/z2021.0248 |
| URN: | urn:nbn:de:hebis:04-z2021-02489 |
| DDC: | 510 Mathematik |
| Titel (trans.): | Hochdimensionale, robuste, heteroskedastische Variablenwahl mit dem adaptiven LASSO und Anwendungen für die Regression mit zufälligen Koeffizienten |
| Publikationsdatum: | 2021-06-29 |
| Lizenz: | https://creativecommons.org/licenses/by-nc-nd/4.0/ |
| Schlagwörter: |
|---|
| sparsity, variable selection, robust regression, high-dimensional regression, linear, sign-consistency, heteroscedasticity, adaptive LASSO, Huber loss |
Summary:
In this thesis, theoretical results for the adaptive LASSO in high-dimensional, sparse linear regression models with potentially heavy-tailed and heteroscedastic errors are developed. In doing so, the empirical pseudo Huber loss is considered as loss function and the main focus is sign-consistency of the resulting estimator. Simulations illustrate the favorable numerical performance of the proposed methodology in comparison to the ordinary adaptive LASSO. Subsequently, those results are applied to the linear random coefficient regression model, more precisely to the means, variances and covariances of the coefficients. Furthermore, sufficient conditions for the identifiability of the first and second moments, as well as asymptotic results for a fixed number of coefficients are given.
 | Das Dokument ist im Internet frei zugänglich - Hinweise zu den Nutzungsrechten |