A Class of Locally and Globally Robust Regression Estimates
作者:
Nelida Ferretti,
Diana Kelmansky,
VictorJ. Yohai,
RubenH. Zamar,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1999)
卷期:
Volume 94,
issue 445
页码: 174-188
ISSN:0162-1459
年代: 1999
DOI:10.1080/01621459.1999.10473834
出版商: Taylor & Francis Group
关键词: Bounded influence;Breakdown point;Maximum bias;Robust regression
数据来源: Taylor
摘要:
We present a new class of regression estimates called generalized τ estimates. These estimates are defined by minimizing the τ scale of the weighted residuals, with weights that penalize high-leverage observations. Like the τ estimates, the generalized τ estimates utilize for their definition two loss functions, ρ1and ρ2, which together with the weights can be chosen to achieve simultaneously high breakdown point, finite gross error sensitivity, and high efficiency. We recommend, however, choosing these functions so as to control the bias behavior of the estimate for a large range of possible contaminations and then boosting the efficiency by a simple least squares reweighting step. The generalized τ estimate with loss functions ρ1and ρ2is related to the Hill–RyanGMestimate with a loss function ρ, which is a linear combination of ρ1and ρr. In fact, both estimates have the same influence function and asymptotic distribution under the central model. We show that a certain generalized τ estimate has good maximum bias behavior and performs well in an extensive Monte Carlo simulation study and three numerical examples.
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