The Conditional Breakdown Properties of Robust Local Polynomial Estimators

Nonparametric regression techniques provide an e ective way of identifying and examiningstructure in regression data The standard approaches to nonparametric regression suchas 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 obseravions