The DOI matches its Crossref record; 20 of the 20 references it cites were found in a registry or an index.
Relative Curvature Measures of Nonlinearity
Abstract
Summary: Simple relative curvature measures of nonlinearity are developed to measure the extent of the nonlinearity in a model-experimental design-parameterization combination. We review the geometric aspects of linear and nonlinear least squares and, using the geometric concept of curvature, compute the maximum relative intrinsic curvature of the solution locus as well as the maximum relative parameter-effects curvature. The relative curvatures are independent of scale changes of the data and of the parameters so they can be used to compare different data sets as well as different parameterizations of the same data set. The methods are applied to 24 published nonlinear data sets, and in all cases it is found that the intrinsic curvature is less than the parameter-effects curvature. The nonlinearity measures of Beale (1960) and the bias expressions developed by Box (1971) are shown to be related to the curvature measures.
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
Cites
Linear Statistical Inference and its Applications: Second Editon
Rao, C. R. (1973) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316436 · Cited by 10,489
Mathematical Methods of Statistics.
Geary, R. C., & Cramer, H. (1947) · The Economic Journal · doi:10.2307/2226151 · Cited by 5,927
Nonlinear Parameter Estimation
Chambers, J. M., & Bard, Y. (1975) · Technometrics · doi:10.2307/1268363 · Cited by 2,158
Nonlinear Parameter Estimation
Brubaker, T. A., & O'Keefe, K. R. (1979) · Analytical Chemistry · doi:10.1021/ac50049a796 · Cited by 2,134
EFRON, B., & HINKLEY, D. V. (1978) · Biometrika · doi:10.1093/biomet/65.3.457 · Cited by 952
DESIGN OF EXPERIMENTS IN NON-LINEAR SITUATIONS
BOX, G. E. P., & LUCAS, H. L. (1959) · Biometrika · doi:10.1093/biomet/46.1-2.77 · Cited by 738
Locally Optimal Designs for Estimating Parameters
Chernoff, H. (1953) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177728915 · Cited by 645
Linear least squares solutions by householder transformations
Businger, P., & Golub, G. H. (1965) · Numerische Mathematik · doi:10.1007/bf01436084 · Cited by 508
Confidence Regions in Non-Linear Estimation
Beale, E. M. L. (1960) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1960.tb00353.x · Cited by 478
Dud, A Derivative-Free Algorithm for Nonlinear Least Squares
Ralston, M. L., & Jennrich, R. I. (1978) · Technometrics · doi:10.1080/00401706.1978.10489610 · Cited by 364
Cited by
Riemann manifold langevin and hamiltonian monte carlo methods
Girolami, M., & Calderhead, B. (2011) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2010.00765.x · Cited by 1,473
Metadata
- Authors
- Bates, D. M., & Watts, D. G.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1980-09-01
- Volume
- 42
- Issue
- 1
- Pages
- 1-16
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W199310666
- Cited by
- 600
- References
- 20
- FWCI
- 8.19
- 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: Relative Curvature Measures of Nonlinearity. https://app.cochat.ai/papers/10.1111/j.2517-6161.1980.tb01094.x
- The paper
- Bates, D. M., & Watts, D. G. (1980). Relative Curvature Measures of Nonlinearity. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/j.2517-6161.1980.tb01094.x
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.
