The extended Bregman divergence and parametric estimation

Minimization of suitable statistical distances (between the data and model densities) is a useful technique in field robust inference. Apart from class ϕ-divergences, Bregman divergence extensively used for this purpose. However, since density must have linear presence term involving both densities structure, several divergences cannot be captured by usual form. We provide an extension considering exponent function as argument rather than itself. Many divergences, that are not ordinarily can accommodated within extended description. Using formulation, one develop many new families which may In particular, through application extension, we propose GSB family. explore applicability minimum estimator discrete parametric models. Simulation studies real examples provided to demonstrate performance substantiate theory developed.