Equivariant variance estimation for multiple change-point model

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)3811-3853
Number of pages43
JournalElectronic Journal of Statistics
Volume17
Issue number2
DOIs
StatePublished - 2023

Keywords

  • Change-point detection
  • inference
  • minimax
  • quadratic estimator
  • total variation
  • unbiasedness

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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