  A robust minimax test for two composite hypotheses, which are determined by
the neighborhoods of two nominal distributions with respect to a set of
distances - called $\alpha-$divergence distances, is proposed. Sion's minimax
theorem is adopted to characterize the saddle value condition. Least favorable
distributions, the robust decision rule and the robust likelihood ratio test
are derived. If the nominal probability distributions satisfy a symmetry
condition, the design procedure is shown to be simplified considerably. The
parameters controlling the degree of robustness are bounded from above and the
bounds are shown to be resulting from a solution of a set of equations. The
simulations performed evaluate and exemplify the theoretical derivations.
