The DOI matches its Crossref record.
When the Data are Functions
Abstract
A datum is often a continuous function x(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 for p-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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Mislevy, R. J., Behrens, J. T., Dicerbo, K. E., & Levy, R. (2012) · Zenodo · doi:10.5281/zenodo.3554641 · Cited by 139
Metadata
- Authors
- Ramsay, J. O.
- Venue
- Psychometrika
- Publisher
- Cambridge University Press (CUP)
- Published
- 1982-12
- Volume
- 47
- Issue
- 4
- Pages
- 379-396
- ISSN
- 0033-3123 (ISSN-L)
- 1860-0980
- OpenAlex
- W2025122406
- Cited by
- 299
- References
- 0
- FWCI
- 2.37
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: When the Data are Functions. https://app.cochat.ai/papers/10.1007/bf02293704
- The paper
- Ramsay, J. O. (1982). When the Data are Functions. Psychometrika. https://doi.org/10.1007/bf02293704
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
