Detection of changes in the mean function

Abstract

In this chapter, we present a methodology for the detection of changes in the mean of functional observations. At its core is a significance test for testing the null hypothesis of a constant functional mean against the alternative of a changing mean. We also show how to locate the change points if the null hypothesis is rejected. Our methodology is readily implemented using the R package fda. The null distribution of the test statistic is asymptotically pivotal with a well-known asymptotic distribution going back to the work of Kiefer (1959).