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APPROXIMATING BY THE WISHART DISTRIBUTION

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TÕNU KOLLO^{1} AND D IETRICH VON ROSEN^{2}

^{1} *Department of Mathematical Statistics, University of Tartu,*

J. Liivi Street 2, EE-2400 Tartu, Estonia

^{2} *Department of Mathematics, Uppsala University, Box 480, S-751 06 Uppsala, Sweden*
(Received January 24, 1994; revised February 6, 1995)

**Abstract.**
Approximations of density functions are
considered in the multivariate case. The results are presented with
the help of matrix derivatives, powers of Kronecker products and
Taylor expansions of functions with matrix argument. In particular,
an approximation by the Wishart distribution is discussed. It is
shown that in many situations the distributions should be centred.
The results are applied to the approximation of the distribution of
the sample covariance matrix and to the distribution of the
non-central Wishart distribution.

*Key words and phrases*:
Density approximation, Edgeworth
expansion, multivariate cumulants, Wishart distribution, non-central
Wishart distribution, sample covariance matrix.

**Source**
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