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Robust Estimation Using Modified Huber’s Functions With New Tails
Jiang, Yunlu Wang, You-Gan Fu, Liya Wang, Xueqin
Jiang, Yunlu
Wang, You-Gan
Fu, Liya
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.
Keywords
Breakdown point, Nonnormal data, Relative efficiency, Robustness
Date
2019
Type
Journal article
Journal
Book
Volume
61
Issue
1
Page Range
111-122
Article Number
ACU Department
Institute for Learning Sciences and Teacher Education (ILSTE)
Faculty of Education and Arts
Faculty of Education and Arts
Relation URI
Event URL
Open Access Status
License
File Access
Controlled
Open
Open
Notes
© 2019 American Statistical Association and the American Society for Quality