IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v117y2018icp19-31.html
   My bibliography  Save this article

Simultaneous estimation based on empirical likelihood and general maximum likelihood estimation

Author

Listed:
  • Park, Junyong

Abstract

One typical problem in simultaneous estimation of mean values is estimating means of normal distributions, however when normality or any other distribution is not specified, more robust estimation procedures are demanded. A new estimation procedure is proposed based on empirical likelihood which does not request any specific distributional assumption. The new idea is based on incorporating empirical likelihood with general maximum likelihood estimation. One well-known nonparametric estimator, the linear empirical Bayes estimator, can be interpreted as an estimator based on empirical likelihood under some framework and it is shown that the proposed procedure can improve the linear empirical Bayes estimator. Numerical studies are presented to compare the proposed estimator with some existing estimators. The proposed estimator is applied to the problem of estimating mean values corresponding to high valued observations. Simulations and real data example of gene expression are provided.

Suggested Citation

  • Park, Junyong, 2018. "Simultaneous estimation based on empirical likelihood and general maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 19-31.
    • Handle: RePEc:eee:csdana:v:117:y:2018:i:c:p:19-31
    DOI: 10.1016/j.csda.2017.08.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016794731730172X
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2017.08.003?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. Xianchao Xie & S. C. Kou & Lawrence D. Brown, 2012. "SURE Estimates for a Heteroscedastic Hierarchical Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1465-1479, December.
    2. Junyong Park, 2012. "Nonparametric empirical Bayes estimator in simultaneous estimation of Poisson means with application to mass spectrometry data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 245-265.
    3. Lawrence D. Brown & Eitan Greenshtein & Ya'acov Ritov, 2013. "The Poisson Compound Decision Problem Revisited," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 741-749, June.
    4. Koenker, Roger & Mizera, Ivan, 2014. "Convex Optimization in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i05).
    5. Efron, Bradley, 2009. "Empirical Bayes Estimates for Large-Scale Prediction Problems," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1015-1028.
    6. Erickson Stephen & Sabatti Chiara, 2005. "Empirical Bayes Estimation of a Sparse Vector of Gene Expression Changes," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-27, September.
    7. Efron B. & Tibshirani R. & Storey J.D. & Tusher V., 2001. "Empirical Bayes Analysis of a Microarray Experiment," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1151-1160, December.
    8. Roger Koenker & Ivan Mizera, 2014. "Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 674-685, June.
    9. Park, Junyong, 2014. "Shrinkage estimator in normal mean vector estimation based on conditional maximum likelihood estimators," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 1-6.
    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. Timothy B. Armstrong & Michal Kolesár & Mikkel Plagborg‐Møller, 2022. "Robust Empirical Bayes Confidence Intervals," Econometrica, Econometric Society, vol. 90(6), pages 2567-2602, November.
    2. Feng, Long & Dicker, Lee H., 2018. "Approximate nonparametric maximum likelihood for mixture models: A convex optimization approach to fitting arbitrary multivariate mixing distributions," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 80-91.
    3. Jiafeng Chen, 2022. "Empirical Bayes When Estimation Precision Predicts Parameters," Papers 2212.14444, arXiv.org, revised Apr 2024.
    4. Timothy B. Armstrong & Michal Koles'ar & Mikkel Plagborg-M{o}ller, 2020. "Robust Empirical Bayes Confidence Intervals," Papers 2004.03448, arXiv.org, revised May 2022.
    5. Wang, Yihe & Zhao, Sihai Dave, 2021. "A nonparametric empirical Bayes approach to large-scale multivariate regression," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    6. Li Tan & Cory Koedel, 2019. "The Effects of Differential Income Replacement and Mortality on U.S. Social Security Redistribution," Southern Economic Journal, John Wiley & Sons, vol. 86(2), pages 613-637, October.
    7. Roger Koenker, 2017. "Bayesian deconvolution: an R vinaigrette," CeMMAP working papers 38/17, Institute for Fiscal Studies.
    8. Jiaying Gu & Roger Koenker, 2020. "Invidious Comparisons: Ranking and Selection as Compound Decisions," Papers 2012.12550, arXiv.org, revised Sep 2021.
    9. Michael Gilraine & Jiaying Gu & Robert McMillan, 2021. "A Nonparametric Method for Estimating Teacher Value-Added," Working Papers tecipa-689, University of Toronto, Department of Economics.
    10. Jiaying Gu & Roger Koenker, 2018. "Nonparametric maximum likelihood methods for binary response models with random coefficients," Papers 1811.03329, arXiv.org, revised Jan 2020.
    11. Stéphane Bonhomme & Martin Weidner, 2019. "Posterior average effects," CeMMAP working papers CWP43/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Jiaying Gu & Roger Koenker, 2014. "Unobserved heterogeneity in income dynamics: an empirical Bayes perspective," CeMMAP working papers 43/14, Institute for Fiscal Studies.
    13. Sihai Dave Zhao, 2017. "Integrative genetic risk prediction using non-parametric empirical Bayes classification," Biometrics, The International Biometric Society, vol. 73(2), pages 582-592, June.
    14. Roger Koenker, 2017. "Bayesian deconvolution: an R vinaigrette," CeMMAP working papers CWP38/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. Jiaying Gu & Roger Koenker, 2017. "Rebayes: an R package for empirical bayes mixture methods," CeMMAP working papers 37/17, Institute for Fiscal Studies.
    16. Fox, Jeremy T. & Kim, Kyoo il & Yang, Chenyu, 2016. "A simple nonparametric approach to estimating the distribution of random coefficients in structural models," Journal of Econometrics, Elsevier, vol. 195(2), pages 236-254.
    17. Li, Xiaoou & Chen, Yunxiao & Chen, Xi & Liu, Jingchen & Ying, Zhiliang, 2021. "Optimal stopping and worker selection in crowdsourcing: an adaptive sequential probability ratio test framework," LSE Research Online Documents on Economics 100873, London School of Economics and Political Science, LSE Library.
    18. Jiaying Gu & Roger Koenker, 2017. "Rebayes: an R package for empirical bayes mixture methods," CeMMAP working papers CWP37/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. Jiaying Gu & Roger Koenker & Stanislav Volgushev, 2017. "Testing for homogeneity in mixture models," CeMMAP working papers 39/17, Institute for Fiscal Studies.
    20. Michael Gilraine & Jiaying Gu & Robert McMillan, 2020. "A New Method for Estimating Teacher Value-Added," NBER Working Papers 27094, National Bureau of Economic Research, Inc.

    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:eee:csdana:v:117:y:2018:i:c:p:19-31. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.