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
AuthorsJiang, Yunlu, Wang, You-Gan, Fu, Liya and Wang, Xueqin
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.

KeywordsBreakdown point; Nonnormal data; Relative efficiency; Robustness
Year01 Jan 2019
JournalTechnometrics
Journal citation61 (1), pp. 111-122
PublisherAmerican Statistical Association
ISSN0040-1706
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 accessPublished as non-open access
Research or scholarlyResearch
Page range111-122
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Output statusPublished
Publication dates
Online17 Oct 2018
Publication process dates
Accepted10 May 2018
Deposited11 Jan 2023
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Open
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© 2019 American Statistical Association and the American Society for Quality

Place of publicationUnited States
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