Robust hypothesis testing for modeling errors

We propose a minimax robust hypothesis testing strategy between two composite hypotheses determined by the neighborhoods of two nominal distributions with respect to the squared Hellinger distance. The robust tests obtained are the nonlinearly transformed versions of the nominal likelihood ratios, whereas the least favorable densities are derived in three different regions. In two of them, they are scaled versions of the corresponding nominal densities and in the third region they form a composite version of the two nominal densities. The outcomes and implications of the proposed robust test are discussed through comparisons with the recent literature.