Non-informative priors for the common mean in the one-way random effects model with heterogeneous error variances

The paper develops some objective priors for the common mean in the one-way random effects model with heterogeneous error variances. We derive the first and second order matching priors and reference priors. It turns out that the second order matching prior matches the alternative coverage probabilities up to the second order, and is also an HPD matching prior. However, derived reference priors just satisfy a first order matching criterion. Our simulation studies indicate that the second order matching prior performs better than the reference prior and the Jeffreys prior in terms of matching the target coverage probabilities in a frequentist sense. We also illustrate our results using real data.