Confidence Sets for Parameters of a Linear Model and Dirichlet Averages

A method is suggested for constructing a conservative confidence region for the parameters of a linear model on the basis of a linear estimator. In meta-analytical applications, when the results of independent, but heterogeneous studies are to be combined, this region can be employed with little to no knowledge of error variances. The formulas for the smallest volume and the corresponding critical constant are derived. The required optimization problem is formulated and some properties of its solution are found by using properties of Dirichlet averages. The method is compared to several resampling schemes by Monte Carlo simulation, and particular cases of one or two parameters are examined.