Detecting Changes in the Functional Linear Regression Model

In this paper, we consider the change-point problems for the functional linear model, where the explanatory variable is a random process, and the response is a scalar. Based on the projecting moment estimators of the parameters onto the truncated finite-dimensional space, we propose the detecting statistic and give the estimator of the change-point. In a theoretical investigation, we derive the asymptotic distribution for the proposed detecting statistic, and establish the consistency of the change-point estimate under some mild conditions. Some simulation studies and a real data analysis are conducted to illustrate the finite performance of the proposed testing methods.