Some Point Estimates and Confidence Regions for Multivariate Inter-laboratory Data Analysis

The problem of analyzing multivariate data from inter-laboratory studies is considered when the data are modeled using the heteroscedastic multivariate one-way random effects model. The primary problem of interest is inference concerning the common mean vector, and a secondary problem of interest is inference concerning the inter-laboratory variance component. Under the usual multivariate normality assumption, this work investigates the point estimation of the inter-laboratory variance component, and the computation of a confidence region for the common mean vector. Noting that a full likelihood based analysis presents computational challenges, some computationally tractable solutions are presented, and illustrated with an example.