On propriety of posterior distributions of variance components in small area estimation

In this article, we investigate for various noninformative improper priors the propriety of the resulting posterior distributions of variance components in a mixed normal linear model. We have considered the usual Jeffreysʹ prior, reference priors and Jeffreysʹ prior based on residual likelihood for variance components. The latter prior is recently advocated as a standard default prior for Bayesian analysis using the PROC MIXED procedure of SAS.