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Smooth principal components for investigating changes in covariances over time

Authors


Address for correspondence: Claire Miller, School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, Glasgow, G12 8QW, UK.
E-mail: Claire.Miller@glasgow.ac.uk

Abstract

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.

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