Cumulants and partition lattices v. calculating generalized k-statistics

Abstract

A method is developed for obtaining compact, easily computed and statistically interpretable expressions for the generalized k-statistics associated with multiply-indexed arrays of random variables such as those which arise in variance component analysis. These expressions will be used in the next paper in this series to give formulae for variances and covariances of estimates of components of variance. © 1988, Australian Mathematical Society. All rights reserved.