IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v107y2012icp141-161.html
   My bibliography  Save this article

Improved chi-squared tests for a composite hypothesis

Author

Listed:
  • Kakizawa, Yoshihide

Abstract

The Bartlett-type adjustment is a higher-order asymptotic method for improving the chi-squared approximation to the null distributions of various test statistics. Though three influential papers were published in 1991—Chandra and Mukerjee (1991) [8], Cordeiro and Ferrari (1991) [12] and Taniguchi (1991) [36] in alphabetical order, the only CF-approach has been frequently applied in the literature during the last two decades, provided that asymptotic expansion for the null distribution of a given test statistic is available. Revisiting the CM/T-approaches developed in the absence of a nuisance parameter, this paper suggests general adjustments for a class of test statistics that includes, in particular, the likelihood ratio, Rao’s and Wald’s test statistics in the presence of a nuisance parameter.

Suggested Citation

  • Kakizawa, Yoshihide, 2012. "Improved chi-squared tests for a composite hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 141-161.
    • Handle: RePEc:eee:jmvana:v:107:y:2012:i:c:p:141-161
    DOI: 10.1016/j.jmva.2012.01.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12000097
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2012.01.008?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. Kakizawa, Yoshihide & Iwashita, Toshiya, 2008. "A comparison of higher-order local powers of a class of one-way MANOVA tests under general distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1128-1153, July.
    2. Li, Xiao & Wu, Yaohua & Tu, Dongsheng, 2008. "A Bartlett type correction for Wald test in Cox regression model," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2614-2622, November.
    3. Taniguchi, Masanobu, 1988. "Asymptotic expansions of the distributions of some test statistics for Gaussian ARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 27(2), pages 494-511, November.
    4. Kakizawa, Yoshihide, 2011. "Improved additive adjustments for the LR/ELR test statistics," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1245-1255, August.
    5. Audrey Cysneiros & Katya Rodrigues & Gauss Cordeiro & Silvia Ferrari, 2010. "Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models," Statistical Papers, Springer, vol. 51(2), pages 273-284, June.
    6. Mukerjee, Rahul, 1992. "Parametric orthogonality and a Bartlett-type modification for Rao's statistic in the presence of a nuisance parameter," Statistics & Probability Letters, Elsevier, vol. 13(5), pages 397-400, April.
    7. 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.
    8. Taniguchi, Masanobu, 1991. "Third-order asymptomic properties of a class of test statistics under a local alternative," Journal of Multivariate Analysis, Elsevier, vol. 37(2), pages 223-238, May.
    9. Gauss M. Cordeiro & Denise A. Botter & Lúcia P. Barroso & Silvia L. P. Ferrari, 2003. "Three Corrected Score Tests for Generalized Linear Models with Dispersion Covariates," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(4), pages 391-409, November.
    10. 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.
    11. Magdalinos, Michael A., 1992. "Stochastic Expansions and Asymptotic Approximations," Econometric Theory, Cambridge University Press, vol. 8(3), pages 343-367, September.
    12. Cordeiro, Gauss M. & Colosimo, Enrico A., 1999. "Corrected score tests for exponential censored data," Statistics & Probability Letters, Elsevier, vol. 44(4), pages 365-373, October.
    13. 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.
    14. 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.
    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, 2016. "Some integrals involving multivariate Hermite polynomials: Application to evaluating higher-order local powers," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 162-168.
    2. 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.
    3. 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.
    4. Kakizawa, Yoshihide, 2012. "Generalized Cordeiro–Ferrari Bartlett-type adjustment," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2008-2016.
    5. 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.

    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, 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, 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.
    4. 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.
    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. Kakizawa, Yoshihide, 2011. "Improved additive adjustments for the LR/ELR test statistics," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1245-1255, August.
    7. 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.
    8. 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.
    9. Francesco Bravo, "undated". "Bartlett-type Adjustments for Empirical Discrepancy Test Statistics," Discussion Papers 04/14, Department of Economics, University of York.
    10. Tu, Dongsheng & Gross, Alan J., 1996. "A Bartlett-type correction for the subject-years method in comparing survival data to a standard population," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 149-157, August.
    11. 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).
    12. 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.
    13. Noud P.A. van Giersbergen, 2013. "Bartlett correction in the stable second‐order autoregressive model with intercept and trend," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 482-498, November.
    14. Symeonides Spyridon D. & Karavias Yiannis & Tzavalis Elias, 2017. "Size corrected Significance Tests in Seemingly Unrelated Regressions with Autocorrelated Errors," Journal of Time Series Econometrics, De Gruyter, vol. 9(1), pages 1-41, January.
    15. Stelios Arvanitis & Antonis Demos, 2015. "A class of indirect inference estimators: higher‐order asymptotics and approximate bias correction," Econometrics Journal, Royal Economic Society, vol. 18(2), pages 200-241, June.
    16. Robinson, Peter M. & Rossi, Francesca, 2015. "Refinements in maximum likelihood inference on spatial autocorrelation in panel data," Journal of Econometrics, Elsevier, vol. 189(2), pages 447-456.
    17. 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.
    18. Antonis Demos & Stelios Arvanitis, 2010. "A New Class of Indirect Estimators and Bias Correction," DEOS Working Papers 1023, Athens University of Economics and Business.
    19. Brown, Kenneth & Cribari-Neto, Francisco, 1992. "On Hypothesis Testing: A Selective Look at the Lagrange Multiplier, Likelihood Ratio and Wald Tests," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 12(2), November.
    20. repec:aue:wpaper:1214 is not listed on IDEAS
    21. 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.

    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:jmvana:v:107:y:2012:i:c:p:141-161. 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.