Skip to main content
SpringerLink
Log in

Bayesian analysis of restricted penalized empirical likelihood

  • Original paper
  • Published:
Computational Statistics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Bartolucci F (2007) A penalized version of the empirical likelihood ratio for the population mean. Stat Probab Lett 77:104–110

    Article  MathSciNet  Google Scholar 

  • Chang J, Chen SX, Chen X (2015) High dimensional generalized empirical likelihood for moment restrictions with dependent data. J Econ 185:283–304

    Article  MathSciNet  Google Scholar 

  • Chang J, Tang CY, Wu TT (2017) A new scope of penalized empirical likelihood with high-dimensional estimating equations. Ann Stat 46:185–216

    MathSciNet  Google Scholar 

  • Chen SX, Cui H (2006) On Bartlett correction of empirical likelihood in the presence of nuisance parameters. Biometrika 93:215–220

    Article  MathSciNet  Google Scholar 

  • Chen SX, Cui H (2007) On the second properties of empirical likelihood with moment restrictions. J Econ 141:492–516

    Article  MathSciNet  Google Scholar 

  • Chen SX, Peng L, Qin YL (2009) Effects of data dimension on empirical likelihood. Biometrika 96:711–722

    Article  MathSciNet  Google Scholar 

  • DiCiccio TJ, Romano JP (1989) On adjustments based on the signed root of the empirical likelihood ratio statistic. Biometrika 76:447–456

    MathSciNet  MATH  Google Scholar 

  • Ghoreishi SK, Meshkani MR (2014) On SURE estimates in hierarchical models assuming heteroscedasticity for both levels of a two-level normal hierarchical model. J Multivar Anal 132:129–137

    Article  MathSciNet  Google Scholar 

  • Hall P, La Scala B (1990) Methodology and algorithms of empirical likelihood. Int Stat Rev 58:109–127

    Article  Google Scholar 

  • Hjort NL, McKeague I, Van Keilegom I (2009) Extending the scope of empirical likeli-hood. Ann Stat 37:1079–1111

    MATH  Google Scholar 

  • Lahiri SN, Mukhopadhyay S (2012) A penalized empirical likelihood method in high dimensions. Ann Stat 40:2511–2540

    Article  MathSciNet  Google Scholar 

  • Lazar N (2003) Bayesian empirical likelihood. Biometrika 90:319–325

    Article  MathSciNet  Google Scholar 

  • Leng C, Tang CY (2012) Penalized empirical likelihood and growing dimensional general estimating equations. Biometrika 99:703–716

    Article  MathSciNet  Google Scholar 

  • Newey WK, Smith RJ (2004) Higher order properties of GMM and generalized empirical likelihood estimators. Econometrica 72:219–255

    Article  MathSciNet  Google Scholar 

  • Owen A (1990) Empirical likelihood ratio confidence regions. Ann Stat 18:90–120

    Article  MathSciNet  Google Scholar 

  • Owen A (1988) Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75:237–249

    Article  MathSciNet  Google Scholar 

  • Owen A (2001) Empirical Likelihood. Chapman and Hall-CRC, New York

    Book  Google Scholar 

  • Qin J, Lawless J (1994) Empirical likelihood and general estimating equations. Ann Stat 22:300–325

    Article  MathSciNet  Google Scholar 

  • Tang CY, Leng C (2010) Penalized high dimensional empirical likelihood. Biometrika 97:905–920

    Article  MathSciNet  Google Scholar 

  • Tang CY, Wu TT (2014) Nested coordinate descent algorithms for empirical likelihood. J Stat Comput Simul 84(9):1917–1930

    Article  MathSciNet  Google Scholar 

  • Thomas DR, Grunkemeier GR (1957) Confidence interval estimation of survival probabilities for censored data. J Am Stat 70:865–871

    Article  MathSciNet  Google Scholar 

  • Tsao M (2004) Bounds on coverage probabilities of the empirical likelihood ratio confidence regions. Ann Stat 32:1215–1221

    Article  MathSciNet  Google Scholar 

  • Tsao M, Wu F (2013) Empirical likelihood on the full parameter space. Ann Stat 41:2176–2196

    Article  MathSciNet  Google Scholar 

  • Tsao M, Wu F (2014) Extended empirical likelihood for estimating equations. Biometrika 101:703–710

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Science and Research branch, Islamic Azad University, Tehran, Iran

    Mahdieh Bayati

  2. Department of Statistics, University of Qom, Qom, Iran

    Seyed Kamran Ghoreishi

  3. Department of Mathematics and Statistics, University of Calgary, Calgary, Canada

    Jingjing Wu

Authors
  1. Mahdieh Bayati
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seyed Kamran Ghoreishi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jingjing Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seyed Kamran Ghoreishi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bayati, M., Ghoreishi, S.K. & Wu, J. Bayesian analysis of restricted penalized empirical likelihood. Comput Stat 36, 1321–1339 (2021). https://doi.org/10.1007/s00180-020-01046-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00180-020-01046-3

Keywords

Search

Navigation