T. Kollo et D. Vonrosen, A UNIFIED APPROACH TO THE APPROXIMATION OF MULTIVARIATE DENSITIES, Scandinavian journal of statistics, 25(1), 1998, pp. 93-109
Approximation of a density by another density is considered in the cas
e of different dimensionalities of the distributions, The results have
been derived by inverting expansions of characteristic functions with
the help of matrix techniques, The approximations obtained are all fu
nctions of cumulant differences and derivatives of the approximating d
ensity, The multivariate Edgeworth expansion follows from the results
as a special case. Furthermore, the density functions of the trace and
eigenvalues of the sample covariance matrix are approximated by the m
ultivariate normal density and a numerical example is given.