The Annals of Statistics

The Log Likelihood Ratio in Segmented Regression

Paul I. Feder

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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.

Article information

Ann. Statist., Volume 3, Number 1 (1975), 84-97.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62E20: Asymptotic distribution theory
Secondary: 62J05: Linear regression

Regression segmented likelihood ratio testing asymptotic theory


Feder, Paul I. The Log Likelihood Ratio in Segmented Regression. Ann. Statist. 3 (1975), no. 1, 84--97. doi:10.1214/aos/1176343000.

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