On Approximation of Mean and Variance-Covariance Matrices of Transformations of Joint Random Variables.

A rationale for the use or rejection of what is loosely called differential approximations of variance, and the extension of the techniques to a wider realm of applicability is presented. The study also includes a discussion of approximations of the mean and variance-covariance matrix of a joint random variable obtained as a transformation of a given combined random variable whose mean and variance-covariance matrix are known but not necessarily the joint distribution. Four theorems are proved which give both form and rationale for the approximations. Author