Robustness of the likelihood ratio test for a change in simple linear regression

Hyune Ju Kim, Lujing Cai

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


This article examines the robustness of the likelihood ratio tests for a change point in simple linear regression. We first summarize the normal theory of Kim and Siegmund, who have considered the likelihood ratio tests for no change in the regression coefficients versus the alternatives with a change in the intercept alone and with a change in the intercept and slope. We then discuss the robustness of these tests. Using the convergence theory of stochastic processes, we show that the test statistics converge to the same limiting distributions regardless of the underlying distribution. We perform simulations to assess the distributional insensitivity of the test statistics to a Weibull, a lognormal, and a contaminated normal distribution in two different cases: fixed and random independent variables. Numerical examples illustrate that the test has a correct size and retains its power when the distribution is nonnormal. We also study the effects of the independent variable’s configuration with the aid of a numerical example.

Original languageEnglish (US)
Pages (from-to)864-871
Number of pages8
JournalJournal of the American Statistical Association
Issue number423
StatePublished - Sep 1993


  • Asymptotic tail distribution
  • Distributional insensitivity
  • Power
  • Significance level
  • Two-phase regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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