IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v78y2008i9p1119-1127.html
   My bibliography  Save this article

Proper Bayesian estimating equation based on Hilbert space method

Author

Listed:
  • Lin, Lu
  • Tan, Lin

Abstract

This paper uses Hilbert space method to introduce and investigate the validity of Bayesian estimating equation. A validity for Hilbert-based Bayesian estimating function is established via the Hilbert-based unbiasedness and information unbiasedness. As an application, the newly proposed method is adopted to construct an estimating equation for nonlinear regression model. Furthermore, the new notion is employed to lay a theoretical foundation for the penalty-based methods such as penalized likelihood and penalized least squares.

Suggested Citation

  • Lin, Lu & Tan, Lin, 2008. "Proper Bayesian estimating equation based on Hilbert space method," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1119-1127, July.
  • Handle: RePEc:eee:stapro:v:78:y:2008:i:9:p:1119-1127
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00382-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    2. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
    3. Lu Lin, 2004. "Generalized quasi-likelihood," Statistical Papers, Springer, vol. 45(4), pages 529-544, October.
    4. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
    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. 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.
    2. Jean-Pierre Florens & Anna Simoni, 2021. "Gaussian Processes and Bayesian Moment Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 482-492, March.
    3. Dengke Xu & Zhongzhan Zhang & Liucang Wu, 2014. "Variable selection in high-dimensional double generalized linear models," Statistical Papers, Springer, vol. 55(2), pages 327-347, May.
    4. Siddhartha Chib & Minchul Shin & Anna Simoni, 2022. "Bayesian estimation and comparison of conditional moment models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 740-764, July.
    5. Isaiah Andrews & Anna Mikusheva, 2022. "Optimal Decision Rules for Weak GMM," Econometrica, Econometric Society, vol. 90(2), pages 715-748, March.
    6. Rong Tang & Yun Yang, 2022. "Bayesian inference for risk minimization via exponentially tilted empirical likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1257-1286, September.
    7. Lehmann, Bruce N., 2009. "The role of beliefs in inference for rational expectations models," Journal of Econometrics, Elsevier, vol. 150(2), pages 322-331, June.
    8. F. Giummolè & V. Mameli & E. Ruli & L. Ventura, 2019. "Objective Bayesian inference with proper scoring rules," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 728-755, September.
    9. Kai-Tai Fang & Rahul Mukerjee, 2006. "Empirical-type likelihoods allowing posterior credible sets with frequentist validity: Higher-order asymptotics," Biometrika, Biometrika Trust, vol. 93(3), pages 723-733, September.
    10. Ventura, Laura & Cabras, Stefano & Racugno, Walter, 2009. "Prior Distributions From Pseudo-Likelihoods in the Presence of Nuisance Parameters," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 768-774.
    11. Giuseppe Ragusa, 2007. "Bayesian Likelihoods for Moment Condition Models," Working Papers 060714, University of California-Irvine, Department of Economics.
    12. In Hong Chang & Rahul Mukerjee, 2008. "Bayesian and frequentist confidence intervals arising from empirical-type likelihoods," Biometrika, Biometrika Trust, vol. 95(1), pages 139-147.
    13. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    14. Luo, Yu & Graham, Daniel J. & McCoy, Emma J., 2023. "Semiparametric Bayesian doubly robust causal estimation," LSE Research Online Documents on Economics 117944, London School of Economics and Political Science, LSE Library.
    15. Kai Yang & Xue Ding & Xiaohui Yuan, 2022. "Bayesian empirical likelihood inference and order shrinkage for autoregressive models," Statistical Papers, Springer, vol. 63(1), pages 97-121, February.
    16. Zhichao Liu & Catherine Forbes & Heather Anderson, 2017. "Robust Bayesian exponentially tilted empirical likelihood method," Monash Econometrics and Business Statistics Working Papers 21/17, Monash University, Department of Econometrics and Business Statistics.
    17. Xu, Ke-Li, 2020. "Inference of local regression in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 218(2), pages 532-560.
    18. In Chang & Rahul Mukerjee, 2012. "On the approximate frequentist validity of the posterior quantiles of a parametric function: results based on empirical and related likelihoods," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 156-169, March.
    19. Siddharta Chib & Minchul Shin & Anna Simoni, 2016. "Bayesian Empirical Likelihood Estimation and Comparison of Moment Condition Models," Working Papers 2016-21, Center for Research in Economics and Statistics.
    20. Sanjay Chaudhuri & Malay Ghosh, 2011. "Empirical likelihood for small area estimation," Biometrika, Biometrika Trust, vol. 98(2), pages 473-480.

    More about this item

    Statistics

    Access and download statistics

    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:stapro:v:78:y:2008:i:9:p:1119-1127. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.