The paper develops a comprehensive asymptotic theory for the estimation of a change-point in the mean function of functional observations. We consider both the case of a constant change size, and the case of a change whose size approaches zero, as the sample size tends to infinity. We show how the limit distribution of a suitably defined change-point estimator depends on the size and location of the change. The theoretical insights are confirmed by a simulation study which illustrates the behavior of the estimator in finite samples. © 2009 Elsevier Inc. All rights reserved.
Aue, A., Gabrys, R., Horváth, L., & Kokoszka, P. (2009). Estimation of a change-point in the mean function of functional data. Journal of Multivariate Analysis, 100(10), 2254–2269. https://doi.org/10.1016/j.jmva.2009.04.001