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February 2020 Consistent selection of the number of change-points via sample-splitting
Changliang Zou, Guanghui Wang, Runze Li
Ann. Statist. 48(1): 413-439 (February 2020). DOI: 10.1214/19-AOS1814

Abstract

In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and the optimal penalization magnitude usually varies from the model and error distribution. We propose a data-driven selection criterion that is applicable to most kinds of popular change-point detection methods, including binary segmentation and optimal partitioning algorithms. The key idea is to select the number of change-points that minimizes the squared prediction error, which measures the fit of a specified model for a new sample. We develop a cross-validation estimation scheme based on an order-preserved sample-splitting strategy, and establish its asymptotic selection consistency under some mild conditions. Effectiveness of the proposed selection criterion is demonstrated on a variety of numerical experiments and real-data examples.

Citation

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Changliang Zou. Guanghui Wang. Runze Li. "Consistent selection of the number of change-points via sample-splitting." Ann. Statist. 48 (1) 413 - 439, February 2020. https://doi.org/10.1214/19-AOS1814

Information

Received: 1 November 2017; Revised: 1 October 2018; Published: February 2020
First available in Project Euclid: 17 February 2020

zbMATH: 07196545
MathSciNet: MR4065168
Digital Object Identifier: 10.1214/19-AOS1814

Subjects:
Primary: 62H12

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • February 2020
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