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2019 Bootstrapping the empirical distribution of a stationary process with change-point
Farid El Ktaibi, B. Gail Ivanoff
Electron. J. Statist. 13(2): 3572-3612 (2019). DOI: 10.1214/19-EJS1613

Abstract

When detecting a change-point in the marginal distribution of a stationary time series, bootstrap techniques are required to determine critical values for the tests when the pre-change distribution is unknown. In this paper, we propose a sequential moving block bootstrap and demonstrate its validity under a converging alternative. Furthermore, we demonstrate that power is still achieved by the bootstrap under a non-converging alternative. We follow the approach taken by Peligrad in [14], and avoid assumptions of mixing, association or near epoch dependence. These results are applied to a linear process and are shown to be valid under very mild conditions on the existence of any moment of the innovations and a corresponding condition of summability of the coefficients.

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Farid El Ktaibi. B. Gail Ivanoff. "Bootstrapping the empirical distribution of a stationary process with change-point." Electron. J. Statist. 13 (2) 3572 - 3612, 2019. https://doi.org/10.1214/19-EJS1613

Information

Received: 1 September 2018; Published: 2019
First available in Project Euclid: 1 October 2019

zbMATH: 07113726
MathSciNet: MR4013746
Digital Object Identifier: 10.1214/19-EJS1613

Subjects:
Primary: 62G09, 62M10
Secondary: 60F17, 62G10, 62G30

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Vol.13 • No. 2 • 2019
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