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Activity Number:
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177
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Type:
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Contributed
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Date/Time:
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Tuesday, August 13, 2002 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Nonparametric Statistics*
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| Abstract - #301364 |
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Title:
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The Conditional Breakdown Properties of Robust Local Polynomial Estimators
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Author(s):
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Avi Giloni*+ and Jeffrey Simonoff
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Affiliation(s):
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Yeshiva University and New York University
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Address:
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500 West 185th Street, BH-428, New York, New York, 10033, USA
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Keywords:
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Least absolute values ; nonparametric regression ; Least median of squares ; Least trimmed squares ; M--estimation
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Abstract:
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Nonparametric regression techniques provide an effective way of identifying and examining structure in regression data. The standard approaches to nonparametric regression, such as local polynomial and smoothing spline estimators, are sensitive to unusual observations, and alternatives designed to be resistant to such observations have been proposed as a solution. Unfortunately, there has been little examination of the resistance properties of these proposed estimators. In this paper we examine the breakdown properties of several robust versions of local polynomial estimation. We show that for some estimators the breakdown at any evaluation point depends on the observed distribution of observations and the kernel weight function used. Using synthetic and real data, we show how the breakdown point at an evaluation point provides a useful summary of the resistance of the regression estimator to unusual observations.
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