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Biometrika 1981 68(1):221-226; doi:10.1093/biomet/68.1.221
© 1981 by Biometrika Trust
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Difficulties in obtaining consistent estimators of variance parameters

NICHOLAS P. JEWELL and GILLIAN M. RAAB

Department of Statistics, Princeton University New Jersey
Medical Computing and Statistics Unit, University of Edinburgh

This paper considers the estimation of variances by pooling information from a large number of small samples, when the means are nuisance parameters about which no assumptions or prior knowledge are available. When the variance is proportional to the square of the mean we obtain a consistent estimator from a marginal likelihood. However, this method cannot be generalized to other variance functions. Integrated likelihood, modified likelihood and partial conditional likelihood methods are investigated for this example and suggest methods for the general case when the standard deviation is small compared with the mean.

Key Words: Conditional likelihood • Consistency • Nuisance parameter


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