Open Access
April 2002 Bootrapping robust estimates of regression
Matias Salibian-Barrera, Ruben H. Zamar
Ann. Statist. 30(2): 556-582 (April 2002). DOI: 10.1214/aos/1021379865


We introduce a new computer-intensive method to estimate the distribution of robust regression estimates. The basic idea behind our method is to bootstrap a reweighted representation of the estimates. To obtain a bootstrap method that is asymptotically correct, we include the auxiliary scale estimate in our reweighted representation of the estimates. Our method is computationally simple because for each bootstrap sample we only have to solve a linear system of equations. The weights we use are decreasing functions of the absolute value of the residuals and hence outlying observations receive small weights. This results in a bootstrap method that is resistant to the presence of outliers in the data. The breakdown points of the quantile estimates derived with this method are higher than those obtained with the bootstrap. We illustrate our method on two datasets and we report the results of a Monte Carlo experiment on confidence intervals for the parameters of the linear model.


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Matias Salibian-Barrera. Ruben H. Zamar. "Bootrapping robust estimates of regression." Ann. Statist. 30 (2) 556 - 582, April 2002.


Published: April 2002
First available in Project Euclid: 14 May 2002

zbMATH: 1012.62028
MathSciNet: MR1902899
Digital Object Identifier: 10.1214/aos/1021379865

Primary: 62F35 , 62F40 , 62G09 , 62G20 , 62G35 , 62J05

Keywords: Breakdown point , confidence intervals , regression

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 2 • April 2002
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