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Improved chi-squared tests for a composite hypothesis

  • Kakizawa, Yoshihide
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    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.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 107 (2012)
    Issue (Month): C ()
    Pages: 141-161

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    Handle: RePEc:eee:jmvana:v:107:y:2012:i:c:p:141-161
    DOI: 10.1016/j.jmva.2012.01.008
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    1. 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.
    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. Kakizawa, Yoshihide, 2011. "Improved additive adjustments for the LR/ELR test statistics," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1245-1255, August.
    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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Magdalinos, Michael A., 1992. "Stochastic Expansions and Asymptotic Approximations," Econometric Theory, Cambridge University Press, vol. 8(03), pages 343-367, September.
    11. 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.
    12. 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.
    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.
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