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The Log Likelihood Ratio in Segmented Regression
Open accessAbstract
This paper deals with the asymptotic distribution of the log likelihood ratio statistic in regression models which have different analytical forms in different regions of the domain of the independent variable. It is shown that under suitable identifiability conditions, the asymptotic chi square results of Wilks and Chernoff are applicable. It is shown by example that if there are actually fewer segments than the number assumed in the model, then the least squares estimates are not asymptotically normal and the log likelihood ratio statistic is not asymptotically $\chi^2$. The asymptotic behavior is then more complicated, and depends on the configuration of the observation points of the independent variable.
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Citations
Cited by
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Muggeo, V. M. R. (2003) · Statistics in Medicine · doi:10.1002/sim.1545 · Cited by 2,371
Some aspects of the spline smoothing approach to non-parametric regression curve fitting
Silverman, B. W. (1985) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1985.tb01327.x · Cited by 1,117
PIECEWISE REGRESSION: A TOOL FOR IDENTIFYING ECOLOGICAL THRESHOLDS
Toms, J. D., & Lesperance, M. L. (2003) · Ecology · doi:10.1890/02-0472 · Cited by 1,038
Algorithms for the optimal identification of segment neighborhoods
Auger, I. E., & Lawrence, C. E. (1989) · Bulletin of Mathematical Biology · doi:10.1007/bf02458835 · Cited by 326
Metadata
- Authors
- Feder, P. I.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1975-01-01
- Volume
- 3
- Issue
- 1
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2000586291
- Cited by
- 165
- References
- 0
- FWCI
- 2.36
- Type
- journal article
- Language
- en
- Open access
- bronze
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- CoChat. (2026). Citation check: The Log Likelihood Ratio in Segmented Regression. https://app.cochat.ai/papers/10.1214/aos/1176343000
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- Feder, P. I. (1975). The Log Likelihood Ratio in Segmented Regression. The Annals of Statistics. https://doi.org/10.1214/aos/1176343000
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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