New Perspectives on Centering
Volume 1, Issue 2 (2023), pp. 216–236
Pub. online: 26 April 2023
Type: Statistical Methodology
Open Access
Open Access
Accepted
20 March 2023
20 March 2023
Published
26 April 2023
26 April 2023
Abstract
Data matrix centering is an ever-present yet under-examined aspect of data analysis. Functional data analysis (FDA) often operates with a default of centering such that the vectors in one dimension have mean zero. We find that centering along the other dimension identifies a novel useful mode of variation beyond those familiar in FDA. We explore ambiguities in both matrix orientation and nomenclature. Differences between centerings and their potential interaction can be easily misunderstood. We propose a unified framework and new terminology for centering operations. We clearly demonstrate the intuition behind and consequences of each centering choice with informative graphics. We also propose a new direction energy hypothesis test as part of a series of diagnostics for determining which choice of centering is best for a data set. We explore the application of these diagnostics in several FDA settings.
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