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

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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Bibliographic Details
Main Author: Hermann, Philipp
Contributors: Holzmann, Hajo (Prof. Dr.) (Thesis advisor)
Format: Doctoral Thesis
Language:English
Published: Philipps-Universität Marburg 2021
Subjects:
sparsity
variable selection
robust regression
Mathematik
high-dimensional regression
linear
sign-consistency
heteroscedasticity
adaptive LASSO
Huber loss
Mathematics
Online Access:PDF Full Text
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Description
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.
Physical Description:140 Pages
DOI:10.17192/z2021.0248

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