Restricted maximum likelihood estimation of a common mean and the Mandel–Paule algorithm

Abstract The estimation of a common normal mean on the basis of interlaboratory evaluations is studied when there is an interlaboratory effect. An estimation equation approach due to Mandel and Paule is examined and its theoretical properties are studied. In particular, we show that the Mandel–Paule solution can be interpreted as a simplified version of the restricted maximum likelihood method. It is also demonstrated that the Mandel–Paule algorithm is a generalized Bayes procedure. The results of numerical comparison of these estimators for a special distribution of within-laboratory variances are also reported.

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