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Generalized Cordeiro–Ferrari Bartlett-type adjustment


  • Kakizawa, Yoshihide


The Bartlett-type adjustment is a higher-order asymptotic method for reducing the errors of the chi-squared approximations to the null distributions of various test statistics, which ensures that the resulting test has size α+o(N−1), where 0<α<1 is the significance level and N is the sample size. Recently, Kakizawa (2012) has revisited the Chandra–Mukerjee/Taniguchi adjustments in a unified way, since Chandra and Mukerjee (1991) and Taniguchi (1991b) originally considered the test of the simple null hypothesis, except for Mukerjee (1992). This paper considers a generalization of the adjustment due to Cordeiro and Ferrari (1991).

Suggested Citation

  • Kakizawa, Yoshihide, 2012. "Generalized Cordeiro–Ferrari Bartlett-type adjustment," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2008-2016.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:2008-2016
    DOI: 10.1016/j.spl.2012.06.022

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    References listed on IDEAS

    1. 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.
    2. Kakizawa, Yoshihide, 2011. "Improved additive adjustments for the LR/ELR test statistics," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1245-1255, August.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Magdalinos, Michael A., 1992. "Stochastic Expansions and Asymptotic Approximations," Econometric Theory, Cambridge University Press, vol. 8(03), pages 343-367, September.
    8. Kakizawa, Yoshihide, 2012. "Improved chi-squared tests for a composite hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 141-161.
    9. 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.
    10. Rao, C. Radhakrishna & Mukerjee, Rahul, 1997. "Comparison of LR, Score, and Wald Tests in a Non-IID Setting," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 99-110, January.
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    Cited by:

    1. 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.
    2. 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.


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