A working likelihood approach for robust regression
Journal article
Fu, Liya, Wang, You-Gan and Cai, Fengjing. (2020). A working likelihood approach for robust regression. Statistical Methods in Medical Research. 29(12), pp. 3641-3652. https://doi.org/10.1177/0962280220936310
Authors | Fu, Liya, Wang, You-Gan and Cai, Fengjing |
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Abstract | Robust approach is often desirable in presence of outliers for more efficient parameter estimation. However, the choice of the regularization parameter value impacts the efficiency of the parameter estimators. To maximize the estimation efficiency, we construct a likelihood function for simultaneously estimating the regression parameters and the tuning parameter. The “working” likelihood function is deemed as a vehicle for efficient regression parameter estimation, because we do not assume the data are generated from this likelihood function. The proposed method can effectively find a value of the regularization parameter based on the extent of contamination in the data. We carry out extensive simulation studies in a variety of cases to investigate the performance of the proposed method. The simulation results show that the efficiency can be enhanced as much as 40% when the data follow a heavy-tailed distribution, and reaches as high as 468% for the heteroscedastic variance cases compared to the traditional Huber’s method with a fixed regularization parameter. For illustration, we also analyzed two datasets: one from a diabetics study and the other from a mortality study. |
Keywords | Data driven; Huber’s loss function; robust method; tuning parameter; working likelihood |
Year | 01 Jan 2020 |
Journal | Statistical Methods in Medical Research |
Journal citation | 29 (12), pp. 3641-3652 |
Publisher | SAGE Publications Ltd |
ISSN | 0962-2802 |
Digital Object Identifier (DOI) | https://doi.org/10.1177/0962280220936310 |
PubMed ID | 32662336 |
Web address (URL) | https://journals.sagepub.com/doi/10.1177/0962280220936310 |
Open access | Published as green open access |
Research or scholarly | Research |
Page range | 3641-3652 |
Author's accepted manuscript | License File Access Level Open |
Publisher's version | License All rights reserved File Access Level Controlled |
Output status | Published |
Publication dates | |
Online | 01 Dec 2020 |
Publication process dates | |
Deposited | 11 Jan 2023 |
Additional information | © The Author(s) 2020. |
Place of publication | United Kingdom |
https://acuresearchbank.acu.edu.au/item/8y934/a-working-likelihood-approach-for-robust-regression
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AM_Wang_2020_A_working_likelihood_approach_for_robust.pdf | |
License: CC BY-NC-ND 4.0 | |
File access level: Open |
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