Equivariant variance estimation for multiple change-point model

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. © 2023, Institute of Mathematical Statistics. All rights reserved. ; Open access journal ; This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.