Open Access
2023 Equivariant variance estimation for multiple change-point model
Ning Hao, Yue Selena Niu, Han Xiao
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Electron. J. Statist. 17(2): 3811-3853 (2023). DOI: 10.1214/23-EJS2190


The variance of noise plays an important role in many change-point detection procedures and the associated inferences. Most commonly used variance estimators require strong assumptions on the true mean structure or normality of the error distribution, which may not hold in applications. More importantly, the qualities of these estimators have not been discussed systematically in the literature. In this paper, we introduce a framework of equivariant variance estimation for multiple change-point models. In particular, we characterize the set of all equivariant unbiased quadratic variance estimators for a family of change-point model classes, and develop a minimax theory for such estimators.

Funding Statement

The authors are partially supported by National Science Foundation grants DMS-1722691 (Niu and Hao), CCF-1740858 (Hao), Simons Foundation 524432 (Hao), National Science Foundation grants DMS-2027855 (Xiao), DMS-2052949 (Xiao) and DMS-2319260 (Xiao).


The authors are grateful to the editor, an associate editor, and two anonymous referees for their insightful comments and suggestions.


Download Citation

Ning Hao. Yue Selena Niu. Han Xiao. "Equivariant variance estimation for multiple change-point model." Electron. J. Statist. 17 (2) 3811 - 3853, 2023.


Received: 1 October 2022; Published: 2023
First available in Project Euclid: 11 December 2023

Digital Object Identifier: 10.1214/23-EJS2190

Keywords: change-point detection , inference , minimax , quadratic estimator , Total variation , unbiasedness

Vol.17 • No. 2 • 2023
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