High-dimensional change-point detection with sparse alternatives

Abstract

We consider the problem of detecting a change in mean in a sequence of Gaussian vectors. Under the alternative hypothesis, the change occurs only in some subset of the components of the vector. We propose a test of the presence of a change-point that is adaptive to the number of changing components. Under the assumption that the vector dimension tends to infinity and the length of the sequence grows slower than the dimension of the signal, we obtain the detection boundary for this problem and prove its rate-optimality.

Cited by in corpus (9)

• Selective review of offline change point detection methods
• Change-point detection in panel data via double CUSUM statistic
• Simultaneous multiple change-point and factor analysis for high-dimensional time series
• Oracle Estimation of a Change Point in High Dimensional Quantile Regression
• Estimating a change point in a sequence of very high-dimensional covariance matrices
• Change Detection via Affine and Quadratic Detectors
• Structural Change in Sparsity
• Segmentation of high dimensional means over multi-dimensional change points and connections to regression trees
• Inference on the change point in high dimensional time series models via plug in least squares