IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v20y2018i4d10.1007_s11009-018-9620-9.html
   My bibliography  Save this article

Testing with Exponentially Tilted Empirical Likelihood

Author

Listed:
  • A. Felipe

    (Complutense University of Madrid)

  • N. Martín

    (Complutense University of Madrid)

  • P. Miranda

    (Complutense University of Madrid)

  • L. Pardo

    (Complutense University of Madrid)

Abstract

Imposing restrictions without assuming underlying distributions to modelize complex realities is a valuable methodological tool. However, if a subset of restrictions were not correctly specified, the usual test-statistics for correctly specified models tend to reject erronously a simple null hypothesis. In this setting, we may say that the model suffers from misspecification. We study the behavior of empirical phi-divergence test-statistics, introduced in Balakrishnan et al. Statistics 49:951–977 (2015), by using the exponential tilted empirical likelihood estimators of Schennach Ann Stat 35:634–672 (2007), as a good compromise between the efficiency of the significance level for small sample sizes and the robustness under misspecification.

Suggested Citation

  • A. Felipe & N. Martín & P. Miranda & L. Pardo, 2018. "Testing with Exponentially Tilted Empirical Likelihood," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1319-1358, December.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:4:d:10.1007_s11009-018-9620-9
    DOI: 10.1007/s11009-018-9620-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-018-9620-9
    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/s11009-018-9620-9?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. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Yuichi Kitamura & Taisuke Otsu & Kirill Evdokimov, 2013. "Robustness, Infinitesimal Neighborhoods, and Moment Restrictions," Econometrica, Econometric Society, vol. 81(3), pages 1185-1201, May.
    3. 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.
    4. Altonji, Joseph G & Segal, Lewis M, 1996. "Small-Sample Bias in GMM Estimation of Covariance Structures," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 353-366, July.
    5. Andersen, Torben G & Sorensen, Bent E, 1996. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 328-352, July.
    6. Hall, Alastair R. & Inoue, Atsushi, 2003. "The large sample behaviour of the generalized method of moments estimator in misspecified models," Journal of Econometrics, Elsevier, vol. 114(2), pages 361-394, June.
    7. Lee, Seojeong, 2014. "Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 178(P3), pages 398-413.
    8. Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998. "Information Theoretic Approaches to Inference in Moment Condition Models," Econometrica, Econometric Society, vol. 66(2), pages 333-358, March.
    9. Alastair R. Hall, 2000. "Covariance Matrix Estimation and the Power of the Overidentifying Restrictions Test," Econometrica, Econometric Society, vol. 68(6), pages 1517-1528, November.
    10. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    11. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    12. Domingo Morales & Leandro Pardo, 2001. "Some approximations to power functions of ϕ-divergence tests in parametric models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 249-269, December.
    13. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
    14. Kan, Raymond & Robotti, Cesare, 2008. "Specification tests of asset pricing models using excess returns," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 816-838, December.
    15. Guido W. Imbens, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(3), pages 359-383.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Amor Keziou & Aida Toma, 2021. "A Robust Version of the Empirical Likelihood Estimator," Mathematics, MDPI, vol. 9(8), pages 1-19, April.

    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. Seojeong Lee, 2018. "Asymptotic Refinements of a Misspecification-Robust Bootstrap for Generalized Empirical Likelihood Estimators," Papers 1806.00953, arXiv.org, revised Jun 2018.
    2. Prosper Dovonon, 2016. "Large Sample Properties of the Three-Step Euclidean Likelihood Estimators under Model Misspecification," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 465-514, April.
    3. Lee, Seojeong, 2016. "Asymptotic refinements of a misspecification-robust bootstrap for GEL estimators," Journal of Econometrics, Elsevier, vol. 192(1), pages 86-104.
    4. Lô, Serigne N. & Ronchetti, Elvezio, 2012. "Robust small sample accurate inference in moment condition models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3182-3197.
    5. repec:bla:ecorec:v:91:y:2015:i::p:1-24 is not listed on IDEAS
    6. 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.
    7. Antoine, Bertille & Bonnal, Helene & Renault, Eric, 2007. "On the efficient use of the informational content of estimating equations: Implied probabilities and Euclidean empirical likelihood," Journal of Econometrics, Elsevier, vol. 138(2), pages 461-487, June.
    8. Hwang, Jungbin & Kang, Byunghoon & Lee, Seojeong, 2022. "A doubly corrected robust variance estimator for linear GMM," Journal of Econometrics, Elsevier, vol. 229(2), pages 276-298.
    9. Bruce E. Hansen & Seojeong Lee, 2021. "Inference for Iterated GMM Under Misspecification," Econometrica, Econometric Society, vol. 89(3), pages 1419-1447, May.
    10. Fan, Yanqin & Gentry, Matthew & Li, Tong, 2011. "A new class of asymptotically efficient estimators for moment condition models," Journal of Econometrics, Elsevier, vol. 162(2), pages 268-277, June.
    11. Ramalho Joaquim J.S., 2005. "Small Sample Bias of Alternative Estimation Methods for Moment Condition Models: Monte Carlo Evidence for Covariance Structures," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(1), pages 1-20, March.
    12. Shane M. Sherlund, 2004. "Quasi Empirical Likelihood Estimation of Moment Condition Models," Econometric Society 2004 North American Summer Meetings 507, Econometric Society.
    13. Giuseppe Ragusa, 2011. "Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 406-456, August.
    14. Alain Guay & Florian Pelgrin, 2007. "Using Implied Probabilities to Improve Estimation with Unconditional Moment Restrictions," Cahiers de recherche 0747, CIRPEE.
    15. Smith, Richard J., 2007. "Efficient information theoretic inference for conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 138(2), pages 430-460, June.
    16. Lavergne, Pascal, 2015. "Assessing the Approximate Validity of Moment Restrictions," TSE Working Papers 15-562, Toulouse School of Economics (TSE), revised May 2020.
    17. Chaudhuri, Saraswata & Renault, Eric, 2020. "Score tests in GMM: Why use implied probabilities?," Journal of Econometrics, Elsevier, vol. 219(2), pages 260-280.
    18. Yuichi Kitamura, 2006. "Empirical Likelihood Methods in Econometrics: Theory and Practice," CIRJE F-Series CIRJE-F-430, CIRJE, Faculty of Economics, University of Tokyo.
    19. Patrik Guggenberger & Jinyong Hahn, 2005. "Finite Sample Properties of the Two-Step Empirical Likelihood Estimator," Econometric Reviews, Taylor & Francis Journals, vol. 24(3), pages 247-263.
    20. Whitney K. Newey & Joaquim J.S. Ramalho & Richard J. Smith, 2003. "A symptotic Bias for GMM and GEL Estimators with Estimated Nuisance Parameter," Economics Working Papers 5_2003, University of Évora, Department of Economics (Portugal).
    21. Richard Smith, 2005. "Local GEL methods for conditional moment restrictions," CeMMAP working papers CWP15/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    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:metcap:v:20:y:2018:i:4:d:10.1007_s11009-018-9620-9. 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.