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Improvement on Chi-Squared Approximation by Monotone Transformation


  • Fujisawa, Hironori


It is well known that Bartlett adjustment yields an improvement on the chi-squared approximations to the likelihood ratio test statistics. However, it is not possible to obtain such an improvement for some test statistics. Typical examples are the score test statistic and Hotelling'sT2-statistic. The purpose of the present paper is to give a general method for improving on the chi-squared approximation. The method suggested is based on a monotone transformation.

Suggested Citation

  • Fujisawa, Hironori, 1997. "Improvement on Chi-Squared Approximation by Monotone Transformation," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 84-89, January.
  • Handle: RePEc:eee:jmvana:v:60:y:1997:i:1:p:84-89

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    Cited by:

    1. Cribari-Neto, Francisco & Ferrari, Silvia L. P., 2001. "Monotonic improved critical values for two [chi]2 asymptotic criteria," Economics Letters, Elsevier, vol. 71(3), pages 307-316, June.
    2. Siotani, Minoru & Wakaki, Hirofumi, 2006. "Contributions to multivariate analysis by Professor Yasunori Fujikoshi," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1914-1926, October.
    3. Xu, Jin & Gupta, Arjun K., 2006. "Improved confidence regions for a mean vector under general conditions," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1051-1062, November.
    4. Fujikoshi, Yasunori, 2000. "Transformations with Improved Chi-Squared Approximations," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 249-263, February.


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