Detecting changes in the mean of functional observations

• Main Authors: Robertas Gabrys, Piotr Kokoszka
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: Change point detection; Functional data analysis; Mean of functional data; Significance test Abbreviated Title; Changes in functional mean; Greenland
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.536.6033; http://wami.usu.edu/files/uploads/publications/bb.pdf

Principal component analysis (PCA) has become a fundamental tool of functional data analysis. It represents the functional data as Xi(t) = µ(t) + 1≤`< ∞ ηi,`v`(t), where µ is the common mean, v ` are the eigenfunctions of the covariance operator, and the ηi, ` are the scores. Inferential procedures assume that the mean function µ(t) is the same for all values of i. If, in fact, the observations do not come from one population, but rather their mean changes at some point(s), the results of PCA are confounded by the change(s). It is therefore important to develop a methodol-ogy to test the assumption of a common functional mean. We develop such a test using quantities which can be readily computed in the R package fda. The null distribution of the test statistic is asymptotically pivotal with a well-known asymp-totic distribution. The asymptotic test has excellent finite sample performance. Its application is illustrated on temperature data from Prague, England and Greenland.