Approximations to the distribution of the sample correlation matrix

Authors:
Tõnu Kollo;Kaire Ruul
Affiliations:
Institute of Mathematical Statistics, University of Tartu, J. Liivi Street 2, Tartu 50409, Estonia;Institute of Mathematical Statistics, University of Tartu, J. Liivi Street 2, Tartu 50409, Estonia
Venue:
Journal of Multivariate Analysis
Year:
2003

Citing 2
Cited 2

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Asymptotic expansion of the sample correlation coefficient under nonnormality

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On a symbolic representation of non-central Wishart random matrices with applications

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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.