Some New Estimation Methods for Weighted Regression When There Are Possible Outliers

The problem considered is the robust estimation of the variance parameter in a heteroscedastic linear model. We treat the situation in which the variance is a function of the explanatory variables. To estimate robustly the variance in this case, it is necessary to guard against the influence of outl...

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Bibliographic Details
Published in:Technometrics 1986-08, Vol.28 (3), p.219-230
Main Authors: Giltinan, David M., Carroll, Raymond J., Ruppert, David
Format: Article
Language:English
Subjects:
Bounded influence
Datasets
Estimation methods
Estimators
Exact sciences and technology
Heteroscedasticity
Least squares
Linear inference, regression
Linear models
Linear regression
Mathematics
Maximum likelihood estimation
Parametric models
Point estimators
Probability and statistics
Regression diagnostics
Robust estimation
Sciences and techniques of general use
Statistical variance
Statistics
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Summary:The problem considered is the robust estimation of the variance parameter in a heteroscedastic linear model. We treat the situation in which the variance is a function of the explanatory variables. To estimate robustly the variance in this case, it is necessary to guard against the influence of outliers in the design as well as outliers in the response. By analogy with the homoscedastic regression case, we propose two estimators that do this. Their performances are evaluated on a number of data sets. We had considerable success with estimators that bound the "self-influence"-that is. the influence an observation has on its own fitted value. We conjecture that in other situations (e.g., homoscedastic regression) bounding the selfinfluence will lead to estimators with good robustness properties.
ISSN:0040-1706
1537-2723
DOI:10.1080/00401706.1986.10488129