Testing Composite Null Hypothesis Based on $S$-Divergences

TL;DR

This paper introduces a robust statistical test for composite null hypotheses using the general S-divergence family, extending previous results and analyzing its asymptotic and robustness properties.

Contribution

It develops a new robust testing procedure based on S-divergences for composite null hypotheses, extending prior work and providing theoretical robustness analysis.

Findings

The test has desirable asymptotic properties.

The method demonstrates robustness under parameter restrictions.

An illustrative example in the normal model is provided.

Abstract

We present a robust test for composite null hypothesis based on the general $S$-divergence 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.