The Annals of Statistics
- Ann. Statist.
- Volume 47, Number 4 (2019), 2051-2079.
High-dimensional change-point detection under sparse alternatives
We consider the problem of detecting a change in mean in a sequence of high-dimensional Gaussian vectors. The change in mean may be occurring simultaneously in an unknown subset components. We propose a hypothesis test to detect the presence of a change-point and establish the detection boundary in different regimes under the assumption that the dimension tends to infinity and the length of the sequence grows with the dimension. A remarkable feature of the proposed test is that it does not require any knowledge of the subset of components in which the change in mean is occurring and yet automatically adapts to yield optimal rates of convergence over a wide range of statistical regimes.
Ann. Statist., Volume 47, Number 4 (2019), 2051-2079.
Received: February 2014
Revised: March 2018
First available in Project Euclid: 21 May 2019
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Enikeeva, Farida; Harchaoui, Zaid. High-dimensional change-point detection under sparse alternatives. Ann. Statist. 47 (2019), no. 4, 2051--2079. doi:10.1214/18-AOS1740. https://projecteuclid.org/euclid.aos/1558425639
- Supplement to “High-dimensional change-point detection under sparse alternatives”. The supplementary material  contains omitted proofs and some additional simulation results.