Robust hypothesis testing with squared Hellinger distance

We extend an earlier work of the same authors, which proposes a minimax robust hypothesis testing strategy between two composite hypotheses based on a squared Hellinger distance. We show that without any further restrictions the former four non-linear equations in four parameters, that have to be solved to design the robust test, can be reduced to two equations in two parameters. Additionally, we show that the same equations can be combined into a single equation if the nominal probability density functions satisfy the symmetry condition. The parameters controlling the degree of robustness are bounded from above depending on the nominal distributions and shown to be determined via solving a polynomial equation of degree two. Experiments justify the benefits of the proposed contributions.