IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v36y2021i2d10.1007_s00180-020-01046-3.html
   My bibliography  Save this article

Bayesian analysis of restricted penalized empirical likelihood

Author

Listed:
  • Mahdieh Bayati

    (Islamic Azad University)

  • Seyed Kamran Ghoreishi

    (University of Qom)

  • Jingjing Wu

    (University of Calgary)

Abstract

In this paper, we introduce restricted empirical likelihood and restricted penalized empirical likelihood estimators. These estimators are obtained under both unbiasedness and minimum variance criteria for estimating equations. These scopes produce estimators which have appealing properties and particularly are more robust against outliers than some currently existing estimators. Assuming some prior densities, we develop the Bayesian analysis of the restricted empirical likelihood and the restricted penalized empirical likelihood. Moreover, we provide an EM algorithm to approximate hyper-parameters. Finally, we carry out a simulation study and illustrate the theoretical results for a real data set.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:2:d:10.1007_s00180-020-01046-3
    DOI: 10.1007/s00180-020-01046-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-020-01046-3
    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/s00180-020-01046-3?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. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    2. 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.
    3. Song Xi Chen & Hengjian Cui, 2006. "On Bartlett correction of empirical likelihood in the presence of nuisance parameters," Biometrika, Biometrika Trust, vol. 93(1), pages 215-220, March.
    4. Chenlei Leng & Cheng Yong Tang, 2012. "Penalized empirical likelihood and growing dimensional general estimating equations," Biometrika, Biometrika Trust, vol. 99(3), pages 703-716.
    5. Min Tsao & Fan Wu, 2014. "Extended empirical likelihood for estimating equations," Biometrika, Biometrika Trust, vol. 101(3), pages 703-710.
    6. Ghoreishi, S.K. & Meshkani, M.R., 2014. "On SURE estimates in hierarchical models assuming heteroscedasticity for both levels of a two-level normal hierarchical model," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 129-137.
    7. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
    8. Bartolucci, Francesco, 2007. "A penalized version of the empirical likelihood ratio for the population mean," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 104-110, January.
    9. 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.
    10. Chen, Song Xi & Cui, Hengjian, 2007. "On the second-order properties of empirical likelihood with moment restrictions," Journal of Econometrics, Elsevier, vol. 141(2), pages 492-516, December.
    11. Cheng Yong Tang & Chenlei Leng, 2010. "Penalized high-dimensional empirical likelihood," Biometrika, Biometrika Trust, vol. 97(4), pages 905-920.
    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. 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.
    2. 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.
    3. Tong Tong Wu & Gang Li & Chengyong Tang, 2015. "Empirical Likelihood for Censored Linear Regression and Variable Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 798-812, September.
    4. 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.
    5. Hong Guo & Changliang Zou & Zhaojun Wang & Bin Chen, 2014. "Empirical likelihood for high-dimensional linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(7), pages 921-945, October.
    6. Roberto Baragona & Francesco Battaglia & Domenico Cucina, 2017. "Empirical likelihood ratio in penalty form and the convex hull problem," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 507-529, November.
    7. Tang, Niansheng & Yan, Xiaodong & Zhao, Puying, 2018. "Exponentially tilted likelihood inference on growing dimensional unconditional moment models," Journal of Econometrics, Elsevier, vol. 202(1), pages 57-74.
    8. Xianyang Zhang & Xiaofeng Shao, 2016. "On the coverage bound problem of empirical likelihood methods for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 395-421, March.
    9. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    10. Feng, Sanying & Lian, Heng & Zhu, Fukang, 2016. "Reduced rank regression with possibly non-smooth criterion functions: An empirical likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 139-150.
    11. Tang, Xingyu & Li, Jianbo & Lian, Heng, 2013. "Empirical likelihood for partially linear proportional hazards models with growing dimensions," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 22-32.
    12. Mardi Dungey & Vitali Alexeev & Jing Tian & Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91, pages 1-24, June.
    13. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    14. Ouyang, Jiangrong & Bondell, Howard, 2023. "Bayesian analysis of longitudinal data via empirical likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    15. 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.
    16. Whang, Yoon-Jae, 2006. "Smoothed Empirical Likelihood Methods For Quantile Regression Models," Econometric Theory, Cambridge University Press, vol. 22(2), pages 173-205, April.
    17. Li, Cheng & Jiang, Wenxin, 2016. "On oracle property and asymptotic validity of Bayesian generalized method of moments," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 132-147.
    18. Fang, Jianglin, 2023. "A split-and-conquer variable selection approach for high-dimensional general semiparametric models with massive data," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    19. Zheqi Wang & Dehui Wang & Jianhua Cheng, 2023. "A new autoregressive process driven by explanatory variables and past observations: an application to PM 2.5," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 619-658, June.
    20. Bedoui, Adel & Lazar, Nicole A., 2020. "Bayesian empirical likelihood for ridge and lasso regressions," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).

    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:compst:v:36:y:2021:i:2:d:10.1007_s00180-020-01046-3. 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.