  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.
