The Annals of Statistics
- Ann. Statist.
- Volume 39, Number 3 (2011), 1580-1607.
Change-point in stochastic design regression and the bootstrap
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.
Ann. Statist., Volume 39, Number 3 (2011), 1580-1607.
First available in Project Euclid: 7 June 2011
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Seijo, Emilio; Sen, Bodhisattva. Change-point in stochastic design regression and the bootstrap. Ann. Statist. 39 (2011), no. 3, 1580--1607. doi:10.1214/11-AOS874. https://projecteuclid.org/euclid.aos/1307452129
- Supplementary material: Supplement to “Change-point in stochastic design regression and the bootstrap”. The supplementary file contains a longer version of this paper with all the technical details which were excluded in the present version due to their length.