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June 2011 Change-point in stochastic design regression and the bootstrap
Emilio Seijo, Bodhisattva Sen
Ann. Statist. 39(3): 1580-1607 (June 2011). DOI: 10.1214/11-AOS874

Abstract

In this paper we study the consistency of different bootstrap procedures for constructing confidence intervals (CIs) for the unique jump discontinuity (change-point) in an otherwise smooth regression function in a stochastic design setting. This problem exhibits nonstandard asymptotics, and we argue that the standard bootstrap procedures in regression fail to provide valid confidence intervals for the change-point. We propose a version of smoothed bootstrap, illustrate its remarkable finite sample performance in our simulation study and prove the consistency of the procedure. The m out of n bootstrap procedure is also considered and shown to be consistent. We also provide sufficient conditions for any bootstrap procedure to be consistent in this scenario.

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Emilio Seijo. Bodhisattva Sen. "Change-point in stochastic design regression and the bootstrap." Ann. Statist. 39 (3) 1580 - 1607, June 2011. https://doi.org/10.1214/11-AOS874

Information

Published: June 2011
First available in Project Euclid: 7 June 2011

zbMATH: 1220.62043
MathSciNet: MR2850213
Digital Object Identifier: 10.1214/11-AOS874

Subjects:
Primary: 62G05 , 62G08
Secondary: 62G20

Keywords: Argmax continuous mapping theorem , consistency of the bootstrap , m out of n bootstrap , Nonstandard asymptotics , semiparametric regression , smoothed bootstrap

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 3 • June 2011
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