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Approximations to the distribution of the sample correlation matrix |
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| Authors: | T nu Kollo,Kaire Ruul |
| Affiliation: | Institute of Mathematical Statistics, University of Tartu, J. Liivi Street 2, Tartu 50409, Estonia |
| 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. |
| Keywords: | Multivariate cumulants Multivariate Taylor expansion Matrix derivative Characteristic function of random matrix Multivariate density approximation |
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