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Consensus mean and interval estimators for the common mean. (English) Zbl 1065.62046
Suppose that $$Y_{ij}=\mu + \varepsilon _{ij}$$, where $$\mu$$ is the true unknown common mean and $$\varepsilon _{ij}\sim N(0,\sigma ^2_i)$$ are independent, normally distributed random variables. In this model, the index $$i$$ denotes the method (or serves for the identification of the laboratory) and $$j$$ denotes the repletion of the measurement. The authors propose two statistics for constructing interval estimates of the mean employing the generalized $$p$$-value approach, proposed by K. W. Tsui and S. Weerahandi [J. Am. Stat. Assoc. 84, 602–607 (1989)]. The authors demonstrate the use of their statistics by application of the presented procedures on real data and examine the coverage probabilities of the proposed estimators by means of simulations.
The results obtained suggest that the coverage attains satisfactory values and corresponds to the nominal value better in the case of balanced designs in the sense that the obtained intervals are in the unbalanced case longer. The published considered sample sizes range from 2 to 30.
##### MSC:
 62F25 Parametric tolerance and confidence regions