Online Change-Point Detection for Functional Data

In this article, we propose a CUSUM-type online change-point detection procedure for monitoring a change in the mean function of dependent functional data. Our method is fully nonparametric and does not require dimension reduction for the functional observations. For the proposed sequential monitoring scheme, we provide the limiting distribution of the CUSUM monitoring statistic under the null hypothesis of no change, which yields the threshold to control the global false alarm rate asymptotically. Furthermore, we show that the proposed sequential test has an asymptotic power one. The method is illustrated by means of Monte Carlo simulation studies and an application to a real dataset. Supplementary materials for this article are available online.