Robust regression with asymmetric loss functions
Fu, Liya and Wang, You-Gan. (2021). Robust regression with asymmetric loss functions. Statistical Methods in Medical Research. 30(8), pp. 1800-1815. https://doi.org/10.1177/09622802211012012
|Authors||Fu, Liya and Wang, You-Gan|
In robust regression, it is usually assumed that the distribution of the error term is symmetric or the data are symmetrically contaminated by outliers. However, this assumption is usually not satisfied in practical problems, and thus if the traditional robust methods, such as Tukey's biweight and Huber's method, are used to estimate the regression parameters, the efficiency of the parameter estimation can be lost. In this paper, we construct an asymmetric Tukey's biweight loss function with two tuning parameters and propose a data-driven method to find the most appropriate tuning parameters. Furthermore, we provide an adaptive algorithm to obtain robust and efficient parameter estimates. Our extensive simulation studies suggest that the proposed method performs better than the symmetric methods when error terms follow an asymmetric distribution or are asymmetrically contaminated. Finally, a cardiovascular risk factors dataset is analyzed to illustrate the proposed method.
|Keywords||Asymmetric error distribution; Huber’s loss function; Tukey’s biweight method; outliers; tuning parameters|
|Year||01 Jan 2021|
|Journal||Statistical Methods in Medical Research|
|Journal citation||30 (8), pp. 1800-1815|
|Publisher||SAGE Publications Ltd|
|Digital Object Identifier (DOI)||https://doi.org/10.1177/09622802211012012|
|Web address (URL)||https://journals.sagepub.com/doi/10.1177/09622802211012012|
|Open access||Published as non-open access|
|Research or scholarly||Research|
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|Online||11 May 2021|
|Publication process dates|
|Deposited||11 Jan 2023|
|ARC Funded Research||This output has been funded, wholly or partially, under the Australian Research Council Act 2001|
© The Author(s) 2021.
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the National Science Foundation of China (grant no. 11871390), the Australian Research Council Discovery Project (DP160104292), the Natural Science Basic Research Plan in Shaanxi Province of China (grant no. 2018JQ1006).
|Place of publication||United Kingdom|
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