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

By Mengjia Yu, Xiaohui Chen. Journal of The Royal Statistical Society Series B-statistical Methodology, 2017

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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.

Subfields: Computational Mechanics, Computer Networks and Communications, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e62909cbf260e1720e39eb6b6f5ef263f524daf9