Finite sample change point inference and identification for high-dimensional mean vectors

Mengjia Yu, Xiaohui Chen

Research output: Contribution to journalArticlepeer-review

Abstract

Cumulative sum (CUSUM) statistics are widely used in the change point inference and identification. For the problem of testing for existence of a change point in an independent sample generated from the mean-shift model, we introduce a Gaussian multiplier bootstrap to calibrate critical values of the CUSUM test statistics in high dimensions. The proposed bootstrap CUSUM test is fully data dependent and it has strong theoretical guarantees under arbitrary dependence structures and mild moment conditions. Specifically, we show that with a boundary removal parameter the bootstrap CUSUM test enjoys the uniform validity in size under the null and it achieves the minimax separation rate under the sparse alternatives when the dimension p can be larger than the sample size n. Once a change point is detected, we estimate the change point location by maximising the (Formula presented.) -norm of the generalised CUSUM statistics at two different weighting scales corresponding to covariance stationary and non-stationary CUSUM statistics. For both estimators, we derive their rates of convergence and show that dimension impacts the rates only through logarithmic factors, which implies that consistency of the CUSUM estimators is possible when p is much larger than n. In the presence of multiple change points, we propose a principled bootstrap-assisted binary segmentation (BABS) algorithm to dynamically adjust the change point detection rule and recursively estimate their locations. We derive its rate of convergence under suitable signal separation and strength conditions. The results derived in this paper are non-asymptotic and we provide extensive simulation studies to assess the finite sample performance. The empirical evidence shows an encouraging agreement with our theoretical results.

Original languageEnglish (US)
Pages (from-to)247-270
Number of pages24
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume83
Issue number2
DOIs
StatePublished - Apr 2021

Keywords

  • CUSUM
  • Gaussian approximation
  • binary segmentation
  • bootstrap
  • change point analysis
  • high-dimensional data

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'Finite sample change point inference and identification for high-dimensional mean vectors'. Together they form a unique fingerprint.

Cite this