Abstract #301663

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JSM 2003 Abstract #301663
Activity Number: 56
Type: Contributed
Date/Time: Sunday, August 3, 2003 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #301663
Title: The Conditional Breakdown Properties of L1 Based Local Polynomial Estimators
Author(s): Avi H. Giloni*+ and Jeffrey S. Simonoff
Companies: Yeshiva University and New York University
Address: 500 W 185 St., New York, NY, 10033-3201,
Keywords: least absolute values ; nonparametric regression ; breakdown
Abstract:

Nonparametric regression techniques provide an effective way of identifying and examining structure in regression data. The standard approaches to local polynomial estimators, those based upon the least squares estimator, are sensitive to unusual observations. One proposed approach to robust local polynomial estimators has been local polynomial estimators based upon the L1 estimator. However, there has been little examination of the resistance properties of these proposed estimators. We examine the breakdown properties of the L1 version of robust local polynomial estimation. We show that the breakdown value at any evaluation point depends on the observed distribution of observations and the kernel weight function used. We introduce a new robustness measure for local polynomial regression. Based upon the breakdown value, our new robustness measure, and the ability to calculate the breakdown value, we show under what conditions different kernels provide better robustness properties for the estimator.

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