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

David M. Giltinan, Raymond J. Carroll and David Ruppert
Technometrics
Vol. 28, No. 3 (Aug., 1986), pp. 219-230
DOI: 10.2307/1269077
Stable URL: http://www.jstor.org/stable/1269077
Page Count: 12
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Some New Estimation Methods for Weighted Regression When There Are Possible Outliers
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Abstract

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 self-influence will lead to estimators with good robustness properties.

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