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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...
Պահպանված է:
| Հիմնական հեղինակ: | |
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| Այլ հեղինակներ: | |
| Ձևաչափ: | Dissertation |
| Լեզու: | անգլերեն |
| Հրապարակվել է: |
Philipps-Universität Marburg
2021
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| Խորագրեր: | |
| Առցանց հասանելիություն: | PDF ամբողջական տեքստ |
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Ավելացրեք ցուցիչ
Չկան պիտակներ, Եղեք առաջինը, ով նշում է այս գրառումը!
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| Ամփոփում: | 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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| Ֆիզիկական նկարագրություն: | 140 Seiten |
| DOI: | 10.17192/z2021.0248 |