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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...
में बचाया:
| मुख्य लेखक: | |
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| अन्य लेखक: | |
| स्वरूप: | Dissertation |
| भाषा: | अंग्रेज़ी |
| प्रकाशित: |
Philipps-Universität Marburg
2021
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| विषय: | |
| ऑनलाइन पहुंच: | पीडीएफ पूर्ण पाठ |
| टैग: |
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| सारांश: | 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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| भौतिक वर्णन: | 140 Seiten |
| डिजिटल ऑब्जेक्ट पहचानकर्ता: | 10.17192/z2021.0248 |