Estimation in a simple random effects model with nonnormal distributions

A simple structural model is considered involving the addition of two random variables representing between- and within-group variation. Methods for estimating the cumulants of the two components of variation are proposed, based on homogeneous polynomials in the data. Emphasis is placed on situations in which the number of observations per group is quite small. In some cases an essentially unique estimator is available, whereas in others there is a family of possible consistent estimators. The choice of the polynomial is considered.