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

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Abstract

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.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Statistics, Texas A&M University, College Station, TX, 77843-3143, USA

    Ursula U. Müller

  2. Department of Mathematical Sciences, Indiana University Purdue University at Indianapolis, Indianapolis, IN, 46202-3267, USA

    Hanxiang Peng

  3. Department of Mathematical Sciences, Binghamton University, Binghamton, NY, 13902-6000, USA

    Anton Schick

Authors
  1. Ursula U. Müller
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  2. Hanxiang Peng
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  3. Anton Schick
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Correspondence to Ursula U. Müller.

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Müller, U.U., Peng, H. & Schick, A. Inference about the slope in linear regression: an empirical likelihood approach. Ann Inst Stat Math 71, 181–211 (2019). https://doi.org/10.1007/s10463-017-0632-y

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  • DOI: https://doi.org/10.1007/s10463-017-0632-y

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