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.
Publié le : 2002-04-14
Classification:
Regression,
breakdown point,
confidence intervals,
62F35,
62F40,
62G09,
62G20,
62G35,
62J05
@article{1021379865,
author = {Salibian-Barrera, Matias and Zamar, Ruben H.},
title = {Bootrapping robust estimates of regression},
journal = {Ann. Statist.},
volume = {30},
number = {1},
year = {2002},
pages = { 556-582},
language = {en},
url = {http://dml.mathdoc.fr/item/1021379865}
}
Salibian-Barrera, Matias; Zamar, Ruben H. Bootrapping robust estimates of regression. Ann. Statist., Tome 30 (2002) no. 1, pp. 556-582. http://gdmltest.u-ga.fr/item/1021379865/