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Smooth principal components for investigating changes in covariances over time
Author(s) -
Miller Claire,
Bowman Adrian
Publication year - 2012
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2012.01037.x
Subject(s) - covariance , bootstrapping (finance) , principal component analysis , multivariate statistics , variance (accounting) , statistics , covariance function , mathematics , econometrics , function (biology) , principal (computer security) , multivariate analysis of variance , computer science , operating system , accounting , evolutionary biology , business , biology
Summary. The complex interrelated nature of multivariate systems can result in relationships and covariance structures that change over time. Smooth principal components analysis is proposed as a means of investigating whether and how the covariance structure of multiple response variables changes over time, after removing a smooth function for the mean, and this is motivated and illustrated by using data from an aircraft technology study and a lake ecosystem. Inferential procedures are investigated in the cases of independent and dependent errors, with a bootstrapping procedure proposed to detect changes in the direction or variance of components.