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June, 1992 Change-Points in Nonparametric Regression Analysis
Hans-Georg Muller
Ann. Statist. 20(2): 737-761 (June, 1992). DOI: 10.1214/aos/1176348654


Estimators for location and size of a discontinuity or change-point in an otherwise smooth regression model are proposed. The assumptions needed are much weaker than those made in parametric models. The proposed estimators apply as well to the detection of discontinuities in derivatives and therefore to the detection of change-points of slope and of higher order curvature. The proposed estimators are based on a comparison of left and right one-sided kernel smoothers. Weak convergence of a stochastic process in local differences to a Gaussian process is established for properly scaled versions of estimators of the location of a change-point. The continuous mapping theorem can then be invoked to obtain asymptotic distributions and corresponding rates of convergence for change-point estimators. These rates are typically faster than $n^{-1/2}$. Rates of global $L^p$ convergence of curve estimates with appropriate kernel modifications adapting to estimated change-points are derived as a consequence. It is shown that these rates of convergence are the same as if the location of the change-point was known. The methods are illustrated by means of the well known data on the annual flow volume of the Nile river between 1871 and 1970.


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Hans-Georg Muller. "Change-Points in Nonparametric Regression Analysis." Ann. Statist. 20 (2) 737 - 761, June, 1992.


Published: June, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0783.62032
MathSciNet: MR1165590
Digital Object Identifier: 10.1214/aos/1176348654

Primary: 62G05
Secondary: 62G20

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 2 • June, 1992
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