|
Abstract:
|
The problems addressed include the computation of a confidence region for the consensus mean vector, and the estimation of the inter-laboratory variance component matrix. A full likelihood based analysis appears to be computationally challenging. For the point estimation of the inter-laboratory variance component matrix, a simple unbiased estimator is first considered, and then the estimator is modified using appropriate shrinking so as to get an improved estimator in terms of mean squared error. For computing a confidence region for the consensus mean vector, some solutions are obtained by following a "likelihood type" approach, with two modifications: (i) a simplified likelihood function is used by replacing the within-laboratory variance-covariance matrices with the corresponding sample counter parts, and (ii) a parametric bootstrap approach is used to obtain the required percentile for obtaining the confidence region. Numerical results are reported on the coverage probabilities, and illustrative examples are given based on real data as well as simulated data. Furthermore, plots are given for the confidence regions in the bivariate and trivariate cases.
|
