Cumulants of bilinear forms and quadratic forms and their applications

Abstract

In this paper, mixed cumulants of general bilinear forms, quadratic forms and linear forms are given up to order 4. These results are useful in deriving approximations to the distributions of sums of squares and F-ratios from unbalanced analysis of variance models from non-normal universes. As an illustration, the results are applied to derive mixed cumulants of sums of squares in a three stages nested unbalanced random effects models from non-normal universes.