IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v71y2019i1d10.1007_s10463-017-0632-y.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-017-0632-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10463-017-0632-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Peng, Hanxiang & Schick, Anton, 2018. "Asymptotic normality of quadratic forms with random vectors of increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 22-39.
    2. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    3. Du, Xiaojie & Schick, Anton, 2018. "Signed rank based empirical likelihood for the symmetric location model," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 40-45.
    4. Karun Adusumilli & Taisuke Otsu, 2017. "Empirical Likelihood for Random Sets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1064-1075, July.
    5. repec:cep:stiecm:/2014/574 is not listed on IDEAS
    6. Xu Guo & Wangli Xu & Lixing Zhu, 2015. "Model checking for parametric regressions with response missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 229-259, April.
    7. Yukun Liu & Changliang Zou & Zhaojun Wang, 2013. "Calibration of the empirical likelihood for high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 529-550, June.
    8. Qinqin Hu & Lu Lin, 2017. "Conditional sure independence screening by conditional marginal empirical likelihood," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 63-96, February.
    9. Mahdieh Bayati & Seyed Kamran Ghoreishi & Jingjing Wu, 2021. "Bayesian analysis of restricted penalized empirical likelihood," Computational Statistics, Springer, vol. 36(2), pages 1321-1339, June.
    10. Liu, Zhi & Xia, Xiaochao & Zhou, Wang, 2015. "A test for equality of two distributions via jackknife empirical likelihood and characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 97-114.
    11. Ying Sheng & Yifei Sun & Chiung‐Yu Huang & Mi‐Ok Kim, 2022. "Synthesizing external aggregated information in the presence of population heterogeneity: A penalized empirical likelihood approach," Biometrics, The International Biometric Society, vol. 78(2), pages 679-690, June.
    12. Jianglin Fang & Wanrong Liu & Xuewen Lu, 2018. "Empirical likelihood for heteroscedastic partially linear single-index models with growing dimensional data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 255-281, April.
    13. Segers, J.J.J. & van den Akker, R. & Werker, B.J.M., 2008. "Improving Upon the Marginal Empirical Distribution Functions when the Copula is Known," Other publications TiSEM 950a8cda-8f8c-43a9-a5c2-8, Tilburg University, School of Economics and Management.
    14. Changliang Zou & Liuhua Peng & Long Feng & Zhaojun Wang, 2014. "Multivariate sign-based high-dimensional tests for sphericity," Biometrika, Biometrika Trust, vol. 101(1), pages 229-236.
    15. Zhao, Yichuan, 2010. "Semiparametric inference for transformation models via empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1846-1858, September.
    16. Francesco Giordano & Soumendra Nath Lahiri & Maria Lucia Parrella, 2014. "GRID for model structure discovering in high dimensional regression," Working Papers 3_231, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.
    17. Yu Shen & Han-Ying Liang, 2018. "Quantile regression and its empirical likelihood with missing response at random," Statistical Papers, Springer, vol. 59(2), pages 685-707, June.
    18. Varron, Davit, 2016. "Empirical likelihood confidence tubes for functional parameters in plug-in estimation," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 100-118.
    19. Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.
    20. Zhang, Jia & Shi, Haoming & Tian, Lemeng & Xiao, Fengjun, 2019. "Penalized generalized empirical likelihood in high-dimensional weakly dependent data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 270-283.
    21. Muller, Ursula & Van Keilegom, Ingrid, 2013. "Efficient quantile regression with auxiliary information," LIDAM Discussion Papers ISBA 2013011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:aistmt:v:71:y:2019:i:1:d:10.1007_s10463-017-0632-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.