Local Linear kernel estimation for discontinuous nonparametric regression functions

Jiti Gao; Anthony N. Pettitt; Rodney C.L. Wolff

doi:10.1080/03610929808832261

Local Linear kernel estimation for discontinuous nonparametric regression functions

Jiti Gao, Anthony N. Pettitt, Rodney C.L. Wolff

Research output: Contribution to journal › Article › Research › peer-review

Abstract

In this paper, we consider using a local linear (LL) smoothing method to estimate a class of discontinuous regression functions. We establish the asymptotic normality of the integrated square error (ISE) of a LL-type estimator and show that the ISE has an asymptotic rate of convergence as good as for smooth functions, and the asymptotic rate of convergence of the ISE of the LL estimator is better than that of the Nadaraya-Watson (NW) and the Gasser-Müller (GM) estimators.

Original language	English
Pages (from-to)	2871-2894
Number of pages	24
Journal	Communications in Statistics - Theory and Methods
Volume	27
Issue number	12
DOIs	https://doi.org/10.1080/03610929808832261
Publication status	Published - 1 Jan 1998

Keywords

Discontinuous regression function
Integrated square error
Kernel estimation
Local linear smoothing
Nonparametric regression

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10.1080/03610929808832261

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keywords = "Discontinuous regression function, Integrated square error, Kernel estimation, Local linear smoothing, Nonparametric regression",

author = "Jiti Gao and Pettitt, {Anthony N.} and Wolff, {Rodney C.L.}",

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AU - Gao, Jiti

AU - Pettitt, Anthony N.

AU - Wolff, Rodney C.L.

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AB - In this paper, we consider using a local linear (LL) smoothing method to estimate a class of discontinuous regression functions. We establish the asymptotic normality of the integrated square error (ISE) of a LL-type estimator and show that the ISE has an asymptotic rate of convergence as good as for smooth functions, and the asymptotic rate of convergence of the ISE of the LL estimator is better than that of the Nadaraya-Watson (NW) and the Gasser-Müller (GM) estimators.

KW - Discontinuous regression function

KW - Integrated square error

KW - Kernel estimation

KW - Local linear smoothing

KW - Nonparametric regression

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JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 12

ER -

Local Linear kernel estimation for discontinuous nonparametric regression functions

Abstract

Keywords

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