Probability seminar: Change-Points in High Dimensional Settings
SM3, School of Mathematics
Claudia Kirch, KIT
While there is considerable work on change-point analysis in univariate time series, more and more data being collected comes from high dimensional multivariate settings. One way to develop an asymptotic framework for such data is to use a Panel data setting where the number of dimensions increases with the sample size. Using contiguous alternatives in such a setup we can compare the asymptotic power of such projection procedures (including an oracle projection on the one hand and a random projection on the other hand) with a Panel statistic that uses the full multivariate information. If information is available to constrain the search region of the test, corresponding projections can lead to a considerable gain in power. All procedures depend on the unknown covariance structure between components whose estimation is very problematic in high dimensional situations, and the possible presence of change-points only further increases these difficulties. If the covariance assumptions made are violated, it not only leads to huge size problems for the Panel statistics but also to a massive power loss, where by looking at contiguous alternatives, the asymptotic power effectively becomes equivalent to choosing a random search direction to apply a univariate test. The size of projections procedures on the other hand is robust with respect to the unknown covariance structure between channels. At the same time while the power can also be affected by misspecification, the impact is often considerably smaller. The theoretic results will be accompagnied by small sample simulations.
This is joint work with John Aston (University of Cambridge).