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Improved additive adjustments for the LR/ELR test statistics

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  • 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
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    References listed on IDEAS

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    1. Cordeiro, Gauss M., 1993. "General matrix formulae for computing Bartlett corrections," Statistics & Probability Letters, Elsevier, vol. 16(1), pages 11-18, January.
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    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. 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.
    7. 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.
    8. Francesco Bravo, "undated". "Bartlett-type Adjustments for Empirical Discrepancy Test Statistics," Discussion Papers 04/14, Department of Economics, University of York.
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    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.

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