  Nested error regression models are useful tools for analysis of grouped data,
especially in the case of small area estimation. This paper suggests a nested
error regression model using uncertain random effects in which the random
effect in each area is expressed as a mixture of a normal distribution and a
positive mass at $0$. For estimation of the model parameters and prediction of
the random effects, an objective Bayesian inference is proposed by setting
non-informative prior distributions on the model parameters. Under mild
sufficient conditions, it is shown that the posterior distribution is proper
and the posterior variances are finite, confirming the validity of posterior
inference. To generate samples from the posterior distribution, we provide the
Gibbs sampling method with familiar forms for all the full conditional
distributions. This paper also addresses the problem of predicting finite
population means, and a sampling-based method is suggested to tackle this
issue. Finally, the proposed model is compared with the conventional nested
error regression model through simulation and empirical studies.
