  For small area estimation of area-level data, the Fay-Herriot model is
extensively used as a model based method. In the Fay-Herriot model, it is
conventionally assumed that the sampling variances are known whereas estimators
of sampling variances are used in practice. Thus, the settings of knowing
sampling variances are unrealistic and several methods are proposed to overcome
this problem. In this paper, we assume the situation where the direct
estimators of the sampling variances are available as well as the sample means.
Using these information, we propose a Bayesian yet objective method producing
shrinkage estimation of both means and variances in the Fay-Herriot model. We
consider the hierarchical structure for the sampling variances and we set
uniform prior on model parameters to keep objectivity of the proposed model.
For validity of the posterior inference, we show under mild conditions that the
posterior distribution is proper and has finite variances. We investigate the
numerical performance through simulation and empirical studies.
