  In this paper a new family of minimum divergence estimators based on the
Bregman divergence is proposed. The popular density power divergence (DPD)
class of estimators is a sub-class of Bregman divergences. We propose and study
a new sub-class of Bregman divergences called the exponentially weighted
divergence (EWD). Like the minimum DPD estimator, the minimum EWD estimator is
recognised as an M-estimator. This characterisation is useful while discussing
the asymptotic behaviour as well as the robustness properties of this class of
estimators. Performances of the two classes are compared -- both through
simulations as well as through real life examples. We develop an estimation
process not only for independent and homogeneous data, but also for
non-homogeneous data. General tests of parametric hypotheses based on the
Bregman divergences are also considered. We establish the asymptotic null
distribution of our proposed test statistic and explore its behaviour when
applied to real data. The inference procedures generated by the new EWD
divergence appear to be competitive or better that than the DPD based
procedures.
