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ESTIMATING THE ROOT OF A NONPARAMETRIC REGRESSION FUNCTION IN A ROBUST FASHION
Author(s) -
He Xuming
Publication year - 1990
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1990.tb01014.x
Subject(s) - nonparametric statistics , nonparametric regression , estimator , regression function , robustness (evolution) , mathematics , regression , statistics , rate of convergence , robust regression , econometrics , regression analysis , computer science , computer network , biochemistry , chemistry , channel (broadcasting) , gene
Summary For a nonparametric regression model y = m(x) + e with n independent observations, we analyze a robust method of finding the root of m(x) based on an M ‐estimation first discussed by Härdle & Gasser (1984). It is shown here that the robustness properties (minimaxity and breakdown function) of such an estimate are quite analogous to those of an M ‐estimator in the simple location model, but the rate of convergence is somewhat limited due to the nonparametric nature of the problem.