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

Author

Listed:
  • Ursula U. Müller

    (Texas A&M University)

  • Hanxiang Peng

    (Indiana University Purdue University at Indianapolis)

  • Anton Schick

    (Binghamton University)

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.

Suggested Citation

  • Ursula U. Müller & Hanxiang Peng & Anton Schick, 2019. "Inference about the slope in linear regression: an empirical likelihood approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 181-211, February.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:1:d:10.1007_s10463-017-0632-y
    DOI: 10.1007/s10463-017-0632-y
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    References listed on IDEAS

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    1. Muller, Ursula & Van Keilegom, Ingrid, 2012. "Efficient parameter estimation in regression with missing responses," LIDAM Reprints ISBA 2012010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Koul H. L. & Susarla V., 1983. "Adaptive Estimation In Linear Regression," Statistics & Risk Modeling, De Gruyter, vol. 1(4-5), pages 379-400, May.
    3. Song Xi Chen & Liang Peng & Ying-Li Qin, 2009. "Effects of data dimension on empirical likelihood," Biometrika, Biometrika Trust, vol. 96(3), pages 711-722.
    4. Peng, Hanxiang & Schick, Anton, 2005. "Efficient estimation of linear functionals of a bivariate distribution with equal, but unknown marginals: the least-squares approach," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 385-409, August.
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