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Approximations to the distribution of the sample correlation matrix

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  • Kollo, Tõnu
  • Ruul, Kaire

Abstract

In this article, multivariate density expansions for the sample correlation matrix R are derived. The density of R is expressed through multivariate normal and through Wishart distributions. Also, an asymptotic expansion of the characteristic function of R is derived and the main terms of the first three cumulants of R are obtained in matrix form. These results make it possible to obtain asymptotic density expansions of multivariate functions of R in a direct way.

Suggested Citation

  • Kollo, Tõnu & Ruul, Kaire, 2003. "Approximations to the distribution of the sample correlation matrix," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 318-334, May.
    • Handle: RePEc:eee:jmvana:v:85:y:2003:i:2:p:318-334
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    References listed on IDEAS

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    1. Kollo, T. & Neudecker, H., 1993. "Asymptotics of Eigenvalues and Unit-Length Eigenvectors of Sample Variance and Correlation Matrices," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 283-300, November.
    2. Tönu Kollo & Dietrich Rosen, 1995. "Approximating by the Wishart distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 767-783, December.
    3. Tõnu Kollo & Dietrich Von Rosen, 1998. "A Unified Approach to the Approximation of Multivariate Densities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 93-109, March.
    4. Boik, Robert J., 1998. "A Local Parameterization of Orthogonal and Semi-Orthogonal Matrices with Applications," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 244-276, November.
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    Cited by:

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    2. Di Nardo, Elvira, 2014. "On a symbolic representation of non-central Wishart random matrices with applications," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 121-135.
    3. 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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