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High-dimensional, robust, heteroscedastic variable selection with the adaptive LASSO, and applications to random coefficient regression

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 o...

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Glavni autor: Hermann, Philipp
Daljnji autori: Holzmann, Hajo (Prof. Dr.) (Savjetnik disertacije)
Format: Dissertation
Jezik:engleski
Izdano: Philipps-Universität Marburg 2021
Teme:
robust regression
sign-consistency
Mathematik
linear
heteroscedasticity
sparsity
high-dimensional regression
Huber loss
variable selection
adaptive LASSO
Mathematics
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Opis
Sažetak: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.
Opis fizičkog objekta:140 Seiten
Digitalni identifikator objekta:10.17192/z2021.0248

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