Inference for high-dimensional linear expectile regression with de-biased method
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913196350111744 |
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| author | Li, Xiang Li, Yu-Ning Zhang, Li-Xin Zhao, Jun |
| author_facet | Li, Xiang Li, Yu-Ning Zhang, Li-Xin Zhao, Jun |
| contents | In this paper, we address the inference problem in high-dimensional linear expectile regression. We transform the expectile loss into a weighted-least-squares form and apply a de-biased strategy to establish Wald-type tests for multiple constraints within a regularized framework. Simultaneously, we construct an estimator for the pseudo-inverse of the generalized Hessian matrix in high dimension with general amenable regularizers including Lasso and SCAD, and demonstrate its consistency through a new proof technique. We conduct simulation studies and real data applications to demonstrate the efficacy of our proposed test statistic in both homoscedastic and heteroscedastic scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07267 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inference for high-dimensional linear expectile regression with de-biased method Li, Xiang Li, Yu-Ning Zhang, Li-Xin Zhao, Jun Methodology 62F05, 62F12, 62J12 In this paper, we address the inference problem in high-dimensional linear expectile regression. We transform the expectile loss into a weighted-least-squares form and apply a de-biased strategy to establish Wald-type tests for multiple constraints within a regularized framework. Simultaneously, we construct an estimator for the pseudo-inverse of the generalized Hessian matrix in high dimension with general amenable regularizers including Lasso and SCAD, and demonstrate its consistency through a new proof technique. We conduct simulation studies and real data applications to demonstrate the efficacy of our proposed test statistic in both homoscedastic and heteroscedastic scenarios. |
| title | Inference for high-dimensional linear expectile regression with de-biased method |
| topic | Methodology 62F05, 62F12, 62J12 |
| url | https://arxiv.org/abs/2401.07267 |