Premium
Detecting changes in the mean of functional observations
Author(s) -
Berkes István,
Gabrys Robertas,
Horváth Lajos,
Kokoszka Piotr
Publication year - 2009
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2009.00713.x
Subject(s) - functional data analysis , principal component analysis , mathematics , functional principal component analysis , statistics , null distribution , test statistic , statistic , population , sample mean and sample covariance , null hypothesis , covariance , statistical hypothesis testing , demography , estimator , sociology
Summary. Principal component analysis has become a fundamental tool of functional data analysis. It represents the functional data as X i ( t )= μ ( t )+Σ 1≤ l <∞ η i , l + v l ( t ), where μ is the common mean, v l are the eigenfunctions of the covariance operator and the η i , l 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 principal component analysis are confounded by the change(s). It is therefore important to develop a methodology 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 asymptotic distribution. The asymptotic test has excellent finite sample performance. Its application is illustrated on temperature data from England.