IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v80y2017i1d10.1007_s00184-016-0593-9.html
   My bibliography  Save this article

Fiducial inference in the classical errors-in-variables model

Author

Listed:
  • Liang Yan

    (Beijing Institute of Technology)

  • Rui Wang

    (Beijing Institute of Technology)

  • Xingzhong Xu

    (Beijing Institute of Technology
    Beijing Institute of Technology)

Abstract

For the slope parameter of the classical errors-in-variables model, existing interval estimations with finite length will have confidence level equal to zero because of the Gleser–Hwang effect. Especially when the reliability ratio is low and the sample size is small, the Gleser–Hwang effect is so serious that it leads to the very liberal coverages and the unacceptable lengths of the existing confidence intervals. In this paper, we obtain two new fiducial intervals for the slope. One is based on a fiducial generalized pivotal quantity and we prove that this interval has the correct asymptotic coverage. The other fiducial interval is based on the method of the generalized fiducial distribution. We also construct these two fiducial intervals for the other parameters of interest of the classical errors-in-variables model and introduce these intervals to a hybrid model. Then, we compare these two fiducial intervals with the existing intervals in terms of empirical coverage and average length. Simulation results show that the two proposed fiducial intervals have better frequency performance. Finally, we provide a real data example to illustrate our approaches.

Suggested Citation

  • Liang Yan & Rui Wang & Xingzhong Xu, 2017. "Fiducial inference in the classical errors-in-variables model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 93-114, January.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:1:d:10.1007_s00184-016-0593-9
    DOI: 10.1007/s00184-016-0593-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-016-0593-9
    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/s00184-016-0593-9?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. Jeffrey R. Thompson & Randy L. Carter, 2007. "An Overview of Normal Theory Structural Measurement Error Models," International Statistical Review, International Statistical Institute, vol. 75(2), pages 183-198, August.
    2. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    3. Schneeweiss, H., 1982. "Note on Creasy's confidence limits for the gradient in the linear functional relationship," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 155-158, March.
    4. Hannig, Jan & Iyer, Hari & Patterson, Paul, 2006. "Fiducial Generalized Confidence Intervals," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 254-269, March.
    5. Wandler, Damian V. & Hannig, Jan, 2011. "Fiducial inference on the largest mean of a multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 87-104, January.
    6. Francq, Bernard G. & Govaerts, Bernadette, 2014. "Measurement methods comparison with errors-in-variables regressions. From horizontal to vertical OLS regression, review and new perspectives," LIDAM Reprints ISBA 2014015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    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. Hannig, Jan & Lai, Randy C.S. & Lee, Thomas C.M., 2014. "Computational issues of generalized fiducial inference," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 849-858.
    2. Liang Yan & Rui Wang & Xingzhong Xu, 2017. "A new confidence interval in errors-in-variables model with known error variance," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2204-2221, September.
    3. Lanqing Hong & Zhi-Sheng Ye & Ran Ling, 2018. "Environmental Risk Assessment of Emerging Contaminants Using Degradation Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(3), pages 390-409, September.
    4. Anastasiou, Andreas, 2017. "Bounds for the normal approximation of the maximum likelihood estimator from m-dependent random variables," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 171-181.
    5. Denter, Philipp & Sisak, Dana, 2015. "Do polls create momentum in political competition?," Journal of Public Economics, Elsevier, vol. 130(C), pages 1-14.
    6. Salgado Alfredo, 2018. "Incomplete Information and Costly Signaling in College Admissions," Working Papers 2018-23, Banco de México.
    7. Albrecht, James & Anderson, Axel & Vroman, Susan, 2010. "Search by committee," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1386-1407, July.
    8. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    9. Li, Xinmin & Wang, Juan & Liang, Hua, 2011. "Comparison of several means: A fiducial based approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1993-2002, May.
    10. Simon Bruhn & Thomas Grebel & Lionel Nesta, 2023. "The fallacy in productivity decomposition," Journal of Evolutionary Economics, Springer, vol. 33(3), pages 797-835, July.
    11. Wim J. van der Linden, 2019. "Lord’s Equity Theorem Revisited," Journal of Educational and Behavioral Statistics, , vol. 44(4), pages 415-430, August.
    12. Yuliang Yin & Bingbing Wang, 2016. "The Agreement between the Generalized Value and Bayesian Evidence in the One-Sided Testing Problem," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-7, May.
    13. Simar, Léopold & Wilson, Paul, 2022. "Modern Tools for Evaluating the Performance of Health-Care Providers," LIDAM Discussion Papers ISBA 2022006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Baey, Charlotte & Didier, Anne & Lemaire, Sébastien & Maupas, Fabienne & Cournède, Paul-Henry, 2013. "Modelling the interindividual variability of organogenesis in sugar beet populations using a hierarchical segmented model," Ecological Modelling, Elsevier, vol. 263(C), pages 56-63.
    15. Tasche, Dirk, 2013. "Bayesian estimation of probabilities of default for low default portfolios," Journal of Risk Management in Financial Institutions, Henry Stewart Publications, vol. 6(3), pages 302-326, July.
    16. Diers, Dorothea & Linde, Marc & Hahn, Lukas, 2016. "Addendum to ‘The multi-year non-life insurance risk in the additive reserving model’ [Insurance Math. Econom. 52(3) (2013) 590–598]: Quantification of multi-year non-life insurance risk in chain ladde," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 187-199.
    17. Anastasiou, Andreas, 2017. "Bounds for the normal approximation of the maximum likelihood estimator from m -dependent random variables," LSE Research Online Documents on Economics 83635, London School of Economics and Political Science, LSE Library.
    18. Hirschberg, Joe & Lye, Jenny, 2017. "Inverting the indirect—The ellipse and the boomerang: Visualizing the confidence intervals of the structural coefficient from two-stage least squares," Journal of Econometrics, Elsevier, vol. 199(2), pages 173-183.
    19. Serguei Kaniovski & Alexander Zaigraev, 2018. "The probability of majority inversion in a two-stage voting system with three states," Theory and Decision, Springer, vol. 84(4), pages 525-546, June.
    20. Hsin-I Lee & Hungyen Chen & Hirohisa Kishino & Chen-Tuo Liao, 2016. "A Reference Population-Based Conformance Proportion," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 684-697, December.

    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:metrik:v:80:y:2017:i:1:d:10.1007_s00184-016-0593-9. 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.