Publikationsserver der Universitätsbibliothek Marburg

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.)
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


variable selection, Huber loss, adaptive LASSO, sign-consistency, heteroscedasticity, sparsity, robust regression, high-dimensional regression, linear

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.

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