Extra Seminar Mathematics - Dr. G. Pan

Title:
Multiple Change Point Detection for Correlated High-Dimensional Observations
via the Largest Eigenvalue

Abstract:
We propose to deal with a mean vector change point detection problem from a
new perspective via the largest eigenvalue when the data dimension p is comparable
to the sample size n. An optimization approach is proposed to figure out both the
unknown number of change points and multiple change point positions simultaneously.
Moreover, an adjustment term is introduced to handle sparse signals when the change
only appears in few components out of the p dimensions. The computation time
is controlled at O(n²) by adopting a dynamic programming, regardless of the true

number of change points k_{0. Theoretical results are developed and various simulations} are conducted to show the effectiveness of our method.