A UNIFIED APPROACH TO THE APPROXIMATION OF MULTIVARIATE DENSITIES

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.