IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v82y2012i4p833-839.html
   My bibliography  Save this article

On standardizing the signed root log likelihood ratio statistic

Author

Listed:
  • Jiang, L.
  • Wong, A.C.M.

Abstract

A simple connection between the Bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant of the p∗ formula–an approximate conditional density for the maximum likelihood estimate given an exact or an approximate ancillary statistic–was established in Barndorff-Nielsen and Cox (1984). In this paper, the explicit form of the normalizing constant of the p∗ formula for the scalar parameter model is derived. By change of variables, the mean and variance of the signed root log likelihood ratio statistic are obtained explicitly, and, hence, tail probabilities can be calculated from the standardized signed root log likelihood ratio statistic. Examples are used to illustrate the implementation and accuracy of the proposed method.

Suggested Citation

  • Jiang, L. & Wong, A.C.M., 2012. "On standardizing the signed root log likelihood ratio statistic," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 833-839.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:4:p:833-839
    DOI: 10.1016/j.spl.2012.01.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771521200020X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2012.01.010?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. Takesi Hayakawa, 1977. "The likelihood ratio criterion and the asymptotic expansion of its distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 29(1), pages 359-378, December.
    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. Wong, A.C.M., 2013. "A note on Bayesian and frequentist parametric inference for a scalar parameter of interest," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 414-421.

    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. Chesher, Andrew & Dhaene, Geert & Gouriéroux, Christian & Scaillet, Olivier, 1999. "Bartlett Identities Tests," LIDAM Discussion Papers IRES 1999019, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    2. Ogasawara, Haruhiko, 2010. "Asymptotic expansions for the pivots using log-likelihood derivatives with an application in item response theory," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2149-2167, October.
    3. Kakizawa, Yoshihide, 2011. "Improved additive adjustments for the LR/ELR test statistics," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1245-1255, August.
    4. Peter C.B. Phillips & Ye Chen, "undated". "Restricted Likelihood Ratio Tests in Predictive Regression," Cowles Foundation Discussion Papers 1968, Cowles Foundation for Research in Economics, Yale University.
    5. Cribari-Netoa, Francisco & Ferrari, Silvia L. P., 1995. "Bartlett-corrected tests for heteroskedastic linear models," Economics Letters, Elsevier, vol. 48(2), pages 113-118, May.
    6. Ogasawara, Haruhiko, 2016. "Asymptotic expansions for the estimators of Lagrange multipliers and associated parameters by the maximum likelihood and weighted score methods," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 20-37.
    7. Kakizawa, Yoshihide, 2012. "Improved chi-squared tests for a composite hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 141-161.
    8. Artur Lemonte & Silvia Ferrari, 2012. "The local power of the gradient test," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 373-381, April.
    9. Ferrari, Silvia L. P. & Cordeiro, Gauss M. & Uribe-Opazo, Miguel A. & Cribari-Neto, Francisco, 1996. "Improved score tests for one-parameter exponential family models," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 61-71, September.
    10. Kakizawa, Yoshihide, 2017. "Third-order average local powers of Bartlett-type adjusted tests: Ordinary versus adjusted profile likelihood," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 98-120.
    11. Willa W. Chen & Rohit S. Deo, 2009. "The restricted likelihood ratio test at the boundary in autoregressive series," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(6), pages 618-630, November.
    12. Rolf Larsson, 2022. "Bartlett correction of an independence test in a multivariate Poisson model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(4), pages 391-417, November.
    13. Kakizawa, Yoshihide, 2012. "Generalized Cordeiro–Ferrari Bartlett-type adjustment," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2008-2016.

    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:82:y:2012:i:4:p:833-839. 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.