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Some integrals involving multivariate Hermite polynomials: Application to evaluating higher-order local powers

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  • Kakizawa, Yoshihide

Abstract

We present the formula for a certain integral with respect to multivariate Hermite polynomials. Such integrals are used for deriving higher-order local power functions of asymptotically chi-squared tests. As an example, we provide asymptotic expansion for the local power function of Rao’s score test.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:110:y:2016:i:c:p:162-168
    DOI: 10.1016/j.spl.2015.12.014
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    References listed on IDEAS

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    1. 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.
    2. Christopher Withers & Saralees Nadarajah, 2010. "Tilted Edgeworth expansions for asymptotically normal vectors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(6), pages 1113-1142, December.
    3. Mukerjee, Rahul, 1990. "Comparison of tests in the multiparameter case II. A third-order optimality property of Rao's test," Journal of Multivariate Analysis, Elsevier, vol. 33(1), pages 31-48, April.
    4. Withers, Christopher S. & Nadarajah, Saralees, 2012. "Improved confidence regions based on Edgeworth expansions," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4366-4380.
    5. Francesco Bravo, 2003. "Second-order power comparisons for a class of nonparametric likelihood-based tests," Biometrika, Biometrika Trust, vol. 90(4), pages 881-890, December.
    6. Fujikoshi, Yasunori, 1997. "An Asymptotic Expansion for the Distribution of Hotelling'sT2-Statistic under Nonnormality," Journal of Multivariate Analysis, Elsevier, vol. 61(2), pages 187-193, May.
    7. Mukerjee, Rahul, 1990. "Comparison of tests in the multiparameter case I. Second-order power," Journal of Multivariate Analysis, Elsevier, vol. 33(1), pages 17-30, April.
    8. Bravo, Francesco, 2004. "Empirical Likelihood Based Inference With Applications To Some Econometric Models," Econometric Theory, Cambridge University Press, vol. 20(2), pages 231-264, April.
    9. 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.
    10. 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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    Cited by:

    1. C. S. Withers, 2024. "5th-Order Multivariate Edgeworth Expansions for Parametric Estimates," Mathematics, MDPI, vol. 12(6), pages 1-28, March.

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