A robust and efficient variable selection method for linear regression
Journal article
Yang, Zhuoran, Fu, Liya, Wang, You-Gan, Dong, Zhixiong and Jiang, Yunlu. (2021). A robust and efficient variable selection method for linear regression. Journal of Applied Statistics. 49(14), pp. 3677-3692. https://doi.org/10.1080/02664763.2021.1962259
Authors | Yang, Zhuoran, Fu, Liya, Wang, You-Gan, Dong, Zhixiong and Jiang, Yunlu |
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Abstract | Variable selection is fundamental to high dimensional statistical modeling, and many approaches have been proposed. However, existing variable selection methods do not perform well in presence of outliers in response variable or/and covariates. In order to ensure a high probability of correct selection and efficient parameter estimation, we investigate a robust variable selection method based on a modified Huber's function with an exponential squared loss tail. We also prove that the proposed method has oracle properties. Furthermore, we carry out simulation studies to evaluate the performance of the proposed method for both p<n and p>n. Our simulation results indicate that the proposed method is efficient and robust against outliers and heavy-tailed distributions. Finally, a real dataset from an air pollution mortality study is used to illustrate the proposed method. |
Keywords | Oracle properties; penalty function; robustness; variable selection |
Year | 01 Jan 2021 |
Journal | Journal of Applied Statistics |
Journal citation | 49 (14), pp. 3677-3692 |
Publisher | Taylor and Francis Ltd. |
ISSN | 0266-4763 |
Digital Object Identifier (DOI) | https://doi.org/10.1080/02664763.2021.1962259 |
PubMed ID | 36246863 |
PubMed Central ID | PMC9559330 |
Web address (URL) | https://www.tandfonline.com/doi/full/10.1080/02664763.2021.1962259 |
Open access | Published as green open access |
Research or scholarly | Research |
Page range | 3677-3692 |
Publisher's version | License All rights reserved File Access Level Controlled |
Output status | Published |
Publication dates | |
Online | 06 Aug 2021 |
Publication process dates | |
Accepted | 26 Jul 2021 |
Deposited | 13 Jan 2023 |
Supplemental file | License All rights reserved File Access Level Controlled |
ARC Funded Research | This output has been funded, wholly or partially, under the Australian Research Council Act 2001 |
Grant ID | DP160104292 |
Additional information | © 2021 Informa UK Limited, trading as Taylor & Francis Group. |
This research was supported by the National Natural Science Foundation of China (No. 11871390), Australian Research Council Discovery Project (DP160104292), the Fundamental Research Funds for the Central Universities (No. xjj2017180), the Natural Science Basic Research Plan in ShaanxiProvince of China (No. 2018JQ1006) and the Natural Science Foundation of Guangdong (Nos. 2018A030313171, 2019A1515011830). | |
Place of publication | United Kingdom |
https://acuresearchbank.acu.edu.au/item/8y93x/a-robust-and-efficient-variable-selection-method-for-linear-regression
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