Item type:Thesis, Open Access

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

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Date

2021-06-29

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Publisher

Philipps-Universität Marburg
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Abstract

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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Dates
Created: 2021Issued: 2021-06-29Updated: 2021-06-29
DOI
https://doi.org/10.17192/z2021.0248
Faculty
Fachbereich Mathematik und Informatik
Publisher
Philipps-Universität Marburg
Language
eng
Data types
DoctoralThesis
Keywords
variable selectionlinearheteroscedasticityhigh-dimensional regressionsign-consistencyadaptive LASSOHuber lossrobust regressionsparsity
DDC-Numbers
510
License
https://creativecommons.org/licenses/by-nc-nd/4.0/
URI
https://open.uni-marburg.de/handle/10.17192/z2021.0248
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Hermann, Philipp: High-dimensional, robust, heteroscedastic variable selection with the adaptive LASSO, and applications to random coefficient regression. : Philipps-Universität Marburg 2021-06-29. DOI: https://doi.org/10.17192/z2021.0248.

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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 - CC BY NC ND
Except where otherwised noted, this item's license is described as Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 - CC BY NC ND