Title: A new CUSUM type procedure for sequential change detection
Authors: Liyan Xie - The Chinese University of Hong Kong, Shenzhen (China) [presenting]
George Moustakides - Rutgers University (United States)
Yao Xie - Georgia Institute of Technology (United States)
Abstract: The parametric online changepoint detection problem is studied, where the underlying distribution of the streaming data changes from a known distribution to an alternative that is of a known parametric form but with unknown parameters. We propose a joint detection/estimation scheme, which we call Window-Limited CUSUM, that combines the cumulative sum (CUSUM) test with a sliding window-based consistent estimate of the post-change parameters. We characterize the optimal choice of window size and show that the Window-Limited CUSUM enjoys first-order asymptotic optimality. Compared to existing schemes with similar asymptotic optimality properties, our test is far simpler in implementation because it can recursively update the CUSUM statistic by employing the estimate of the post-change parameters. A parallel variant is also proposed that facilitates the practical implementation of the test. Numerical simulations corroborate our theoretical findings.