On the robustness of a divergence based test of simple statistical hypotheses

• Generalizes DPD based tests to the case of the SS-divergence.
• Presents theoretical robustness results for SS-divergence based tests.
• Derives the power and level influence functions of the tests.
• Introduces the chi-square inflation factor in connection with the SS-divergence tests.

The most popular hypothesis testing procedure, the likelihood ratio test, is known to be highly non-robust in many real situations. Basu et al. (2013a) provided an alternative robust procedure of hypothesis testing based on the density power divergence; however, although the robustness properties of the latter test were intuitively argued for by the authors together with extensive empirical substantiation of the same, no theoretical robustness properties were presented in that work. In the present paper we will consider a more general class of tests which forms a superfamily of the procedures described by Basu et al. (2013a). This superfamily derives from the class of SS-divergences recently proposed by Ghosh et al. (2013). In this context we theoretically prove several robustness results of the new class of tests and illustrate them in the normal model. All the theoretical robustness properties of the Basu et al. (2013a) proposal follows as special cases of our results.