ESTIMATING THE ROOT OF A NONPARAMETRIC REGRESSION FUNCTION IN A ROBUST FASHION

Xuming He

doi:10.1111/j.1467-842X.1990.tb01014.x

ESTIMATING THE ROOT OF A NONPARAMETRIC REGRESSION FUNCTION IN A ROBUST FASHION

Xuming He

Arts & Sciences

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Abstract

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.

Original language	English
Pages (from-to)	217-225
Number of pages	9
Journal	Australian Journal of Statistics
Volume	32
Issue number	2
DOIs	https://doi.org/10.1111/j.1467-842X.1990.tb01014.x
State	Published - Jun 1990

Keywords

Asymptotic normality
breakdown function
confidence region
M‐estimation
nonparametric regression
robustness

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10.1111/j.1467-842X.1990.tb01014.x

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AB - 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.

KW - Asymptotic normality

KW - breakdown function

KW - confidence region

KW - M‐estimation

KW - nonparametric regression

KW - robustness

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JO - Australian Journal of Statistics

JF - Australian Journal of Statistics

IS - 2

ER -

ESTIMATING THE ROOT OF A NONPARAMETRIC REGRESSION FUNCTION IN A ROBUST FASHION

Abstract

Keywords

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