A generalized divergence for statistical inference

Abstract

The power divergence (PD) and the density power divergence (DPD) families have proven to be useful tools in the area of robust inference. In this paper, we consider a superfamily of divergences which contains both of these families as special cases. The role of this superfamily is studied in several statistical applications, and desirable properties are identified and discussed. In many cases, it is observed that the most preferred minimum divergence estimator within the above collection lies outside the class of minimum PD or minimum DPD estimators, indicating that this superfamily has real utility, rather than just being a routine generalization. The limitation of the usual first order influence function as an effective descriptor of the robustness of the estimator is also demonstrated in this connection.