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Psychometrika

, Volume 47, Issue 4, pp 379–396 | Cite as

When the data are functions

  • J. O. Ramsay
Article

Abstract

A datum is often a continuous functionx(t) of a variable such as time observed over some interval. One or more such functions are observed for each subject or unit of observation. The extension of classical data analytic techniques designed forp-variate observations to such data is discussed. The essential step is the expression of the classical problem in the language of functional analysis, after which the extension to functions is a straightforward matter. A schematic device called the duality diagram is a very useful tool for describing an analysis and for suggesting new possibilities. Least squares approximation, descriptive statistics, principal components analysis, and canonical correlation analysis are discussed within this broader framework.

Key words

continuous data functional analysis duality diagram 

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Reference notes

  1. Keller, E. & Ostry, D. J. Computerized measurement of tongue dorsum movements with pulsed echo ultrasound(a). Manuscript submitted for publication toJournal of the Acoustical Society of America, 1982.Google Scholar
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Copyright information

© The Psychometric Society 1982

Authors and Affiliations

  • J. O. Ramsay
    • 1
  1. 1.McGill UniversityCanada

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