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Restricted maximum likelihood estimation of a common mean and the Mandel-Paule algorithm. (English) Zbl 0943.62024
Summary: 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 J. Mandel and R. C. Paule [An. Chem. 42, 1194-1197 (1970)] 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.

MSC:
62F12 Asymptotic properties of parametric estimators
62F30 Parametric inference under constraints
62P99 Applications of statistics
62E20 Asymptotic distribution theory in statistics
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