  This paper presents objective priors for robust Bayesian estimation against
outliers based on divergences. The minimum $\gamma$-divergence estimator is
well-known to work well estimation against heavy contamination. The robust
Bayesian methods by using quasi-posterior distributions based on divergences
have been also proposed in recent years. In objective Bayesian framework, the
selection of default prior distributions under such quasi-posterior
distributions is an important problem. In this study, we provide some
properties of reference and moment matching priors under the quasi-posterior
distribution based on the $\gamma$-divergence. In particular, we show that the
proposed priors are approximately robust under the condition on the
contamination distribution without assuming any conditions on the contamination
ratio. Some simulation studies are also presented.
