Bootstrapping Robust Estimates of Regression

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 estimat...

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Bibliographic Details
Published in:The Annals of statistics 2002-04, Vol.30 (2), p.556-582
Main Authors: Salibian-Barrera, Matias, Zamar, Ruben H.
Format: Article
Language:English
Subjects:
Bootstrap resampling
Confidence interval
Datasets
Estimation methods
Exact sciences and technology
Least squares
Linear inference, regression
Linear regression
Mathematics
Nonparametric inference
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Outliers
Parametric inference
Point estimators
Probability and statistics
Regression analysis
Robust Regression
Sciences and techniques of general use
Statistical discrepancies
Statistics
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Summary: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.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1021379865