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High-dimensional Edgeworth expansion of a test statistic on independence and its error bound

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  • Akita, Tomoyuki
  • Jin, Jinghua
  • Wakaki, Hirofumi

Abstract

In this paper, we calculate Edgeworth expansion of a test statistic on independence when some of the parameters are large, and simulate the goodness of fit of its approximation. We also calculate an error bound for Edgeworth expansion. Some tables of the error bound are given, which show that the derived bound is sufficiently small for practical use.

Suggested Citation

  • Akita, Tomoyuki & Jin, Jinghua & Wakaki, Hirofumi, 2010. "High-dimensional Edgeworth expansion of a test statistic on independence and its error bound," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1806-1813, September.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:8:p:1806-1813
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    References listed on IDEAS

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    1. 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.
    2. Fujikoshi, Yasunori, 2000. "Error Bounds for Asymptotic Approximations of the Linear Discriminant Function When the Sample Sizes and Dimensionality are Large," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 1-17, April.
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    Cited by:

    1. Qinwen Zhu & Hui Liu & Chengfeng Sun, 2019. "Edgeworth Expansion For The Distribution Of The Maximum Likelihood Estimate In The Vasicek Model," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-26, March.
    2. Yamada, Yuki & Hyodo, Masashi & Nishiyama, Takahiro, 2017. "Testing block-diagonal covariance structure for high-dimensional data under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 305-316.

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