Inference about the slope in linear regression: an empirical likelihood approach

  • Ursula U. Müller
  • Hanxiang Peng
  • Anton Schick


We present a new, efficient maximum empirical likelihood estimator for the slope in linear regression with independent errors and covariates. The estimator does not require estimation of the influence function, in contrast to other approaches, and is easy to obtain numerically. Our approach can also be used in the model with responses missing at random, for which we recommend a complete case analysis. This suffices thanks to results by Müller and Schick (Bernoulli 23:2693–2719, 2017), which demonstrate that efficiency is preserved. We provide confidence intervals and tests for the slope, based on the limiting Chi-square distribution of the empirical likelihood, and a uniform expansion for the empirical likelihood ratio. The article concludes with a small simulation study.


Efficiency Estimated constraint functions Infinitely many constraints Maximum empirical likelihood estimator Missing responses Missing at random 



We thank two reviewers and the Associate Editor for their knowledgeable comments and suggestions, which helped us improve the paper.


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2017

Authors and Affiliations

  • Ursula U. Müller
    • 1
  • Hanxiang Peng
    • 2
  • Anton Schick
    • 3
  1. 1.Department of StatisticsTexas A&M UniversityCollege StationUSA
  2. 2.Department of Mathematical SciencesIndiana University Purdue University at IndianapolisIndianapolisUSA
  3. 3.Department of Mathematical SciencesBinghamton UniversityBinghamtonUSA

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