Journal Article

Detecting changes in the mean of functional observations

Gabrys, Robertas, Kokoszka, Piotr, Horváth, Lajos, Berkes, István

2009

Overview

Principal component analysis has become a fundamental tool of functional data analysis. It represents the functional data as Xi(t)=μ(t)+Σ1[less-than or equal to]l<[infinity]ηi, l+ vl(t), where μ is the common mean, vl are the eigenfunctions of the covariance operator and the ηi, 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.

• Publisher: Oxford, UK : Blackwell Publishing Ltd,Blackwell Publishing Ltd,Wiley-Blackwell,Blackwell,Royal Statistical Society,Oxford University Press
• Subject: Analysis / Analysis of covariance / Assumptions / Change-point detection / Changes / Covariance / Critical values / Data / Data analysis / Data collection / Distribution / Distribution theory / Eigenfunctions / Eigenvalues / England / Exact sciences and technology / Functional analysis / Functional data analysis / General topics / Mathematical analysis / Mathematical functions / Mathematics / Mean of functional data / Multivariate analysis / Null hypothesis / principal component analysis / Principal components analysis / Probability and statistics / Sciences and techniques of general use / Significance test / Statistical methods / Statistical variance / Statistics / Studies / temperature / Tests / United Kingdom / Weather