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Biometrika 2002 89(4):831-840; doi:10.1093/biomet/89.4.831
© 2002 by Biometrika Trust
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Estimation in a simple random effects model with nonnormal distributions

D.R. Cox1 and Peter Hall2

1 Nuffield College, University of Oxford, Oxford OX1 1PP, U.Kdavid.cox{at}nuffield.oxford.ac.uk 2 Centre for Mathematics and its Applications, Australian National University, Canberra 0200, Australia peter.hall{at}anu.edu.au

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.

Key Words: Components of variance; Cumulant; Group effect; Moment; Nonnormal error distribution; Random effects; U-statistic

Received September 2001. Revised March 2002


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