Robust Estimation Using Modified Huber’s Functions With New Tails
Journal article
Jiang, Yunlu, Wang, You-Gan, Fu, Liya and Wang, Xueqin. (2019). Robust Estimation Using Modified Huber’s Functions With New Tails. Technometrics. 61(1), pp. 111-122. https://doi.org/10.1080/00401706.2018.1470037
Authors | Jiang, Yunlu, Wang, You-Gan, Fu, Liya and Wang, Xueqin |
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Abstract | It is traditionally believed that robustness is obtained by sacrificing efficiency. Estimators with high breakdown point and high efficiency are therefore highly desirable. We investigate a new estimation procedure based on Huber’s robust approach, but with tail functions replaced by the exponential squared loss. The tuning parameters are data-dependent to achieve high efficiency even in nonnormal cases. In the regression framework, we show that our hybrid estimator is of high efficiency, reaching the highest asymptotic breakdown point of 50%. We have also established the n−−√-consistency and asymptotic normality of our estimator under regularity conditions. Extensive numerical studies are carried out to compare the performances of our method and other existing methods in terms of the standard errors and relative efficiency, and the results reveal that the newly proposed method has smaller standard errors and higher relative efficiency than its competitors when the sample size is sufficiently large. Finally, we present three real examples for demonstration. Supplementary materials for the article are available online. |
Keywords | Breakdown point; Nonnormal data; Relative efficiency; Robustness |
Year | 01 Jan 2019 |
Journal | Technometrics |
Journal citation | 61 (1), pp. 111-122 |
Publisher | American Statistical Association |
ISSN | 0040-1706 |
Digital Object Identifier (DOI) | https://doi.org/10.1080/00401706.2018.1470037 |
Web address (URL) | https://www.tandfonline.com/doi/full/10.1080/00401706.2018.1470037 |
Open access | Published as non-open access |
Research or scholarly | Research |
Page range | 111-122 |
Publisher's version | License All rights reserved File Access Level Controlled |
Output status | Published |
Publication dates | |
Online | 17 Oct 2018 |
Publication process dates | |
Accepted | 10 May 2018 |
Deposited | 11 Jan 2023 |
Supplemental file | License File Access Level Open |
Additional information | © 2019 American Statistical Association and the American Society for Quality |
Place of publication | United States |
https://acuresearchbank.acu.edu.au/item/8y929/robust-estimation-using-modified-huber-s-functions-with-new-tails
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Supplemental file
OA_Wang_2019_Robust_Estimation_SupplementaryMaterials.pdf | |
License: CC BY 4.0 | |
File access level: Open |
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