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Asymptotic expansions for the distributions of functions of a correlation matrix

Author

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  • Konishi, Sadanori

Abstract

This paper deals with asymptotic expansions for the non-null distributions of certain test statistics concerning a correlation matrix in a multivariate normal distribution. For this purpose an asymptotic expansion is given for the distribution of a function of the sample correlation matrix. As special cases of the resulting expansion, asymptotic expansions for the distributions of the sample correlation coefficient, Fisher's z-transformation and arcsine transformation are also given.

Suggested Citation

  • Konishi, Sadanori, 1979. "Asymptotic expansions for the distributions of functions of a correlation matrix," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 259-266, June.
    • Handle: RePEc:eee:jmvana:v:9:y:1979:i:2:p:259-266
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    Cited by:

    1. Gerd Christoph & Vladimir V. Ulyanov, 2020. "Second Order Expansions for High-Dimension Low-Sample-Size Data Statistics in Random Setting," Mathematics, MDPI, vol. 8(7), pages 1-28, July.
    2. Ogasawara, Haruhiko, 2006. "Asymptotic expansion of the sample correlation coefficient under nonnormality," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 891-910, February.

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