Testing composite null hypotheses based onS-divergences

Abstract

We present a robust test for composite null hypothesis based on the general Sdivergence family. This requires a non-trivial extension of the results of Ghosh et al. (2015). We derive the asymptotic and theoretical robustness properties of the resulting test along with the properties of the minimum S-divergence estimators under parameter restrictions imposed by the null hypothesis. An illustration in the context of the normal model is also presented.