The Influence Function of Penalized Regression Estimators
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2015
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916590925119488 |
|---|---|
| author | Öllerer, Viktoria Croux, Christophe Alfons, Andreas |
| author_facet | Öllerer, Viktoria Croux, Christophe Alfons, Andreas |
| contents | To perform regression analysis in high dimensions, lasso or ridge estimation are a common choice. However, it has been shown that these methods are not robust to outliers. Therefore, alternatives as penalized M-estimation or the sparse least trimmed squares (LTS) estimator have been proposed. The robustness of these regression methods can be measured with the influence function. It quantifies the effect of infinitesimal perturbations in the data. Furthermore it can be used to compute the asymptotic variance and the mean squared error. In this paper we compute the influence function, the asymptotic variance and the mean squared error for penalized M-estimators and the sparse LTS estimator. The asymptotic biasedness of the estimators make the calculations nonstandard. We show that only M-estimators with a loss function with a bounded derivative are robust against regression outliers. In particular, the lasso has an unbounded influence function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1501_01208 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | The Influence Function of Penalized Regression Estimators Öllerer, Viktoria Croux, Christophe Alfons, Andreas Statistics Theory 62J20, 62J07 To perform regression analysis in high dimensions, lasso or ridge estimation are a common choice. However, it has been shown that these methods are not robust to outliers. Therefore, alternatives as penalized M-estimation or the sparse least trimmed squares (LTS) estimator have been proposed. The robustness of these regression methods can be measured with the influence function. It quantifies the effect of infinitesimal perturbations in the data. Furthermore it can be used to compute the asymptotic variance and the mean squared error. In this paper we compute the influence function, the asymptotic variance and the mean squared error for penalized M-estimators and the sparse LTS estimator. The asymptotic biasedness of the estimators make the calculations nonstandard. We show that only M-estimators with a loss function with a bounded derivative are robust against regression outliers. In particular, the lasso has an unbounded influence function. |
| title | The Influence Function of Penalized Regression Estimators |
| topic | Statistics Theory 62J20, 62J07 |
| url | https://arxiv.org/abs/1501.01208 |