IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i8p1245-1255.html
   My bibliography  Save this article

Improved additive adjustments for the LR/ELR test statistics

Author

Listed:
  • Kakizawa, Yoshihide

Abstract

The Bartlett adjustment, being a simple adjustment through division by the expected value of the test statistic, is commonly used as a general statistical tool to reduce the error of the chi-squared approximation of parametric/empirical likelihood ratio (LR/ELR) test statistic. In this paper, some improved test statistics in the additive forms are presented, whose errors of the chi-squared approximation are , as in the case of the traditional multiplicative Bartlett adjustment, where N is the sample size. By deriving the N-1-difference of the power functions of two tests under a sequence of local alternatives, it is shown that none of several adjustments of the LR/ELR test statistic is uniformly superior. The results are numerically illustrated on specific examples.

Suggested Citation

  • Kakizawa, Yoshihide, 2011. "Improved additive adjustments for the LR/ELR test statistics," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1245-1255, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1245-1255
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211001076
    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. Cordeiro, Gauss M., 1993. "General matrix formulae for computing Bartlett corrections," Statistics & Probability Letters, Elsevier, vol. 16(1), pages 11-18, January.
    2. 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.
    3. Song Chen, 1993. "On the accuracy of empirical likelihood confidence regions for linear regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 621-637, December.
    4. Song Xi Chen & Hengjian Cui, 2006. "On Bartlett correction of empirical likelihood in the presence of nuisance parameters," Biometrika, Biometrika Trust, vol. 93(1), pages 215-220, March.
    5. Kakizawa, Yoshihide, 2010. "Comparison of Bartlett-type adjusted tests in the multiparameter case," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1638-1655, August.
    6. Chen, Song Xi & Cui, Hengjian, 2007. "On the second-order properties of empirical likelihood with moment restrictions," Journal of Econometrics, Elsevier, vol. 141(2), pages 492-516, December.
    7. Chandra, Tapas K. & Mukerjee, Rahul, 1991. "Bartlett-type modification for Rao's efficient score statistic," Journal of Multivariate Analysis, Elsevier, vol. 36(1), pages 103-112, January.
    8. Francesco Bravo, "undated". "Bartlett-type Adjustments for Empirical Discrepancy Test Statistics," Discussion Papers 04/14, Department of Economics, University of York.
    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. Kakizawa, Yoshihide, 2012. "Generalized Cordeiro–Ferrari Bartlett-type adjustment," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2008-2016.
    2. Kakizawa, Yoshihide, 2013. "Third-order local power properties of tests for a composite hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 303-317.
    3. Kakizawa, Yoshihide, 2012. "Improved chi-squared tests for a composite hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 141-161.

    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. 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.
    2. Kakizawa, Yoshihide, 2012. "Improved chi-squared tests for a composite hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 141-161.
    3. Liu, Yukun & Yu, Chi Wai, 2010. "Bartlett correctable two-sample adjusted empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1701-1711, August.
    4. Whang, Yoon-Jae, 2006. "Smoothed Empirical Likelihood Methods For Quantile Regression Models," Econometric Theory, Cambridge University Press, vol. 22(2), pages 173-205, April.
    5. Kakizawa, Yoshihide, 2010. "Comparison of Bartlett-type adjusted tests in the multiparameter case," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1638-1655, August.
    6. Kakizawa, Yoshihide, 2009. "Third-order power comparisons for a class of tests for multivariate linear hypothesis under general distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 473-496, March.
    7. Kakizawa, Yoshihide, 2012. "Generalized Cordeiro–Ferrari Bartlett-type adjustment," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2008-2016.
    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. Zhang, Jia & Shi, Haoming & Tian, Lemeng & Xiao, Fengjun, 2019. "Penalized generalized empirical likelihood in high-dimensional weakly dependent data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 270-283.
    10. Francesco Bravo, "undated". "Empirical likelihood specification testing in linear regression models," Discussion Papers 00/28, Department of Economics, University of York.
    11. Tong Tong Wu & Gang Li & Chengyong Tang, 2015. "Empirical Likelihood for Censored Linear Regression and Variable Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 798-812, September.
    12. 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.
    13. Song Xi Chen & Jiti Gao, 2010. "Simultaneous Testing of Mean and Variance Structures in Nonlinear Time Series Models," School of Economics and Public Policy Working Papers 2010-28, University of Adelaide, School of Economics and Public Policy.
    14. Francesco Bravo, "undated". "Bartlett-type Adjustments for Empirical Discrepancy Test Statistics," Discussion Papers 04/14, Department of Economics, University of York.
    15. Mardi Dungey & Vitali Alexeev & Jing Tian & Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91, pages 1-24, June.
    16. Kakizawa, Yoshihide, 2015. "Third-order local power properties of tests for a composite hypothesis, II," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 99-112.
    17. 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.
    18. Mahdieh Bayati & Seyed Kamran Ghoreishi & Jingjing Wu, 2021. "Bayesian analysis of restricted penalized empirical likelihood," Computational Statistics, Springer, vol. 36(2), pages 1321-1339, June.
    19. Hong Guo & Changliang Zou & Zhaojun Wang & Bin Chen, 2014. "Empirical likelihood for high-dimensional linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(7), pages 921-945, October.
    20. Kun Chen & Ngai Hang Chan & Chun Yip Yau, 2020. "Bartlett correction of frequency domain empirical likelihood for time series with unknown innovation variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1159-1173, October.

    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:81:y:2011:i:8:p:1245-1255. 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.