Equivariant Variance Estimation for Multiple Change-point Model

TL;DR

This paper introduces a new framework for unbiased variance estimation in multiple change-point models that is equivariant and minimax optimal, addressing limitations of existing methods under weaker assumptions.

Contribution

It characterizes all equivariant unbiased quadratic variance estimators and develops a minimax theory for these estimators in change-point models.

Findings

Characterization of all equivariant unbiased quadratic variance estimators.

Development of a minimax theory for variance estimators.

Addresses limitations of traditional estimators under weaker assumptions.

Abstract

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.