IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/107521.html
   My bibliography  Save this paper

Relative error accurate statistic based on nonparametric likelihood

Author

Listed:
  • Camponovo, Lorenzo
  • Matsushita, Yukitoshi
  • Otsu, Taisuke

Abstract

This paper develops a new test statistic for parameters defined by moment conditions that exhibits desirable relative error properties for the approximation of tail area probabilities. Our statistic, called the tilted exponential tilting (TET) statistic, is constructed by estimating certain cumulant generating functions under exponential tilting weights. We show that the asymptotic p-value of the TET statistic can provide an accurate approximation to the p-value of an infeasible saddlepoint statistic, which admits a Lugannani–Rice style adjustment with relative errors of order n −1 both in normal and large deviation regions. Numerical results illustrate the accuracy of the proposed TET statistic. Our results cover both just- and overidentified moment condition models. A limitation of our analysis is that the theoretical approximation results are exclusively for the infeasible saddlepoint statistic, and closeness of the p-values for the infeasible statistic to the ones for the feasible TET statistic is only numerically assessed.

Suggested Citation

  • Camponovo, Lorenzo & Matsushita, Yukitoshi & Otsu, Taisuke, 2021. "Relative error accurate statistic based on nonparametric likelihood," LSE Research Online Documents on Economics 107521, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:107521
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/107521/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    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. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    3. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871532, September.
    4. Bryan W. Brown & Whitney K. Newey, 1998. "Efficient Semiparametric Estimation of Expectations," Econometrica, Econometric Society, vol. 66(2), pages 453-464, March.
    5. 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.
    6. Phillips, P C B, 1980. "The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables," Econometrica, Econometric Society, vol. 48(4), pages 861-878, May.
    7. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    8. Veronika Czellar, 2010. "Accurate and Robust Tests for Indirect Inference," Post-Print hal-00553964, HAL.
    9. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692106, September.
    10. 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.
    11. Veronika Czellar & Elvezio Ronchetti, 2010. "Accurate and Robust Tests for Indirect Inference," Post-Print hal-00585938, HAL.
    12. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692090, September.
    13. Ma, Yanyuan & Ronchetti, Elvezio, 2011. "Saddlepoint Test in Measurement Error Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 147-156.
    14. Veronika Czellar & Elvezio Ronchetti, 2010. "Accurate and Robust Tests for Indirect Inference," Post-Print hal-02313230, HAL.
    15. Veronika Czellar & Elvezio Ronchetti, 2010. "Accurate and robust tests for indirect inference," Biometrika, Biometrika Trust, vol. 97(3), pages 621-630.
    16. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871549, September.
    17. Jens Jensen & Andrew Wood, 1998. "Large Deviation and Other Results for Minimum Contrast Estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(4), pages 673-695, December.
    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. Lorenzo Camponovo & Taisuke Otsu, 2017. "Relative error accurate statistic based on nonparametric likelihood," STICERD - Econometrics Paper Series 593, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Guggenberger, Patrik & Ramalho, Joaquim J.S. & Smith, Richard J., 2012. "GEL statistics under weak identification," Journal of Econometrics, Elsevier, vol. 170(2), pages 331-349.
    3. Aeberhard, William H. & Cantoni, Eva & Heritier, Stephane, 2017. "Saddlepoint tests for accurate and robust inference on overdispersed count data," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 162-175.
    4. Otsu, Taisuke, 2011. "Moderate deviations of generalized method of moments and empirical likelihood estimators," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1203-1216, September.
    5. repec:bla:ecorec:v:91:y:2015:i::p:1-24 is not listed on IDEAS
    6. Hahn, Jinyong & Newey, Whitney K. & Smith, Richard J., 2014. "Neglected heterogeneity in moment condition models," Journal of Econometrics, Elsevier, vol. 178(P1), pages 86-100.
    7. Horowitz, Joel L., 2021. "Bounding the difference between true and nominal rejection probabilities in tests of hypotheses about instrumental variables models," Journal of Econometrics, Elsevier, vol. 222(2), pages 1057-1082.
    8. 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.
    9. Martyn Andrews & Obbey Elamin & Alastair R. Hall & Kostas Kyriakoulis & Matthew Sutton, 2014. "Inference in the Presence of Redundant Moment Conditions and the Impact of Government Health Expenditure on Health Outcomes in England," Economics Discussion Paper Series 1401, Economics, The University of Manchester.
    10. 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.
    11. 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.
    12. Jin, Fei & Lee, Lung-fei, 2019. "GEL estimation and tests of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 208(2), pages 585-612.
    13. Xuexin Wang, 2020. "A new class of tests for overidentifying restrictions in moment condition models," Econometric Reviews, Taylor & Francis Journals, vol. 39(5), pages 495-509, May.
    14. Ronchetti, Elvezio, 2020. "Accurate and robust inference," Econometrics and Statistics, Elsevier, vol. 14(C), pages 74-88.
    15. Lavergne, Pascal, 2015. "Assessing the Approximate Validity of Moment Restrictions," TSE Working Papers 15-562, Toulouse School of Economics (TSE), revised May 2020.
    16. Yuichi Kitamura, 2020. "A Comment on: “On the Informativeness of Descriptive Statistics for Structural Estimates” by Isaiah Andrews, Matthew Gentzkow, and Jesse M. Shapiro," Econometrica, Econometric Society, vol. 88(6), pages 2265-2269, November.
    17. Taisuke Otsu & Chen Qiu, 2018. "Information theoretic approach to high dimensional multiplicative models: Stochastic discount factor and treatment effect," STICERD - Econometrics Paper Series 595, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    18. Guggenberger, Patrik & Smith, Richard J., 2005. "Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification," Econometric Theory, Cambridge University Press, vol. 21(4), pages 667-709, August.
    19. Gubhinder Kundhi & Paul Rilstone, 2015. "Saddlepoint expansions for GEL estimators," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 1-24, March.
    20. Sueishi, Naoya, 2013. "Identification problem of the exponential tilting estimator under misspecification," Economics Letters, Elsevier, vol. 118(3), pages 509-511.
    21. Doko Tchatoka, Firmin Sabro, 2012. "Specification Tests with Weak and Invalid Instruments," MPRA Paper 40185, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ehl:lserod:107521. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    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.